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Math Basic

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Level D

Lighthouse

Math Basic Edition

PROGRAM DIRECTORS Esther Aboud Lauren Noorparvar Yehudis Leitner

Credits Curriculum Writers

Review Team

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Esther Aboud

Middle School Math Instructor M.Ed. in Curriculum and Instruction

5–12 Math/German Teacher Curriculum Writer M.Ed. Learning & Technology

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Lighthouse Math Level D - Basic Edition • ISBN 978-1-955773-97-3 ©Copyright 2021 Lighthouse Curriculum Inc. All rights reserved. Contact Lighthouse Curriculum: Call 718.285.7100 or email info@lighthousecurriculum.com For more information visit www.lighthousecurriculum.com Content developed in collaboration with The Reimagined Classroom

No part of this publication may be reproduced, stored in a retrieval system, stored in a database and/or published in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher. To obtain permission to use portions of material from this publication, please contact Lighthouse Curriculum.

Welcome to the Lighthouse Math Curriculum! Here’s what you’ll find in every chapter:

Introduction and overview of skills at the beginning of each chapter

Clearly coded lessons: blue for the lesson page, red for the exercise page

Daily review at the beginning of every lesson to provide review of previous skills

Learn and Connect helps introduce the concept

Apply provides guided practice as a class

Practice provides plenty of problems to practice the skill

Challenge problems for enrichment and practice

Review for every chapter

Assessment provided for every chapter

7 + 6

A better way to teach Dear Educator, Welcome to the Lighthouse Math Curriculum! What makes our curriculum so unique? Lighthouse Math uses a scaffolded approach to learning and mastering math skills. When provided with a solid foundation, students can retain more information and prepare for the next level of skills.

Instead of separate workbooks and textbooks, students have everything they need built into one place: a softcover book containing 11 chapters, with each lesson containing review, new skills, and practice. All lessons include step-by-step instructions for clarity, giving all teachers - new as well as seasoned - the tools for success. The books are custom illustrated, providing a vibrant learning experience. They are formatted in a way that each grade level can be completed successfully by the culmination of the school year. Lighthouse Math gives teachers the tools they need to teach and gives students everything they need to learn. We at Lighthouse Curriculum are committed to providing support and guidance to our educators. We look forward to hearing from you and are available to answer any questions you may have.

Sincerely, Lighthouse Curriculum Team

1 - 1 | Addition and Subtractio

n Facts

Write the number that comes next .

DAIL Y REVI EW

LEAR N AND CON NECT Addition and subtraction are opposites. When we add, we put two parts together to make a whole. When we subtract, we take one part away from the whole to find the part that is left.

Sam has 9 marbles, and Ron has 3 marbles. How many marbles do they have when they put them all toge ther?

strictly prohibited.

addend + addend =

sum

9 3 12

−

minuend − subtrahend = diffe rence

−

12 3 9

APPL Y

Solve. 1. + 7. −

5 9 12 3

2. +

3 5

−

8 5

7 4

−

11 5

10.

6 2

−

4 1

11.

8 5

−

13 9

12.

1 4

−

12 3

Vocabulary Sum - the answer to an addition proble m Difference - the answer to a subtra ction problem Minuend - a number from which another is to be subtra

cted

Level D

Subtrahend - a number to be subtra cted from another number Addend - a number added to anoth er number

| Chapter 1 - 1

| Lighthouse MAT H

Ron takes his marbles back. How man y marbles does Sam have now?

Table of Contents Chapter 1

1-1

Addition and Subtraction Facts �� 16

1-2

Opposite Operations �� 18

1-3

Rules of Addition and Subtraction �� 20

1-4

Column Addition �� 22

1-5

Counting by 1, 2, 3, and 4 �� 24

1-6

Counting by 5, 10, 25, and 100 �� 26

1-7

Counting Money �� 28

1-8

Chapter Review �� 30

1-9

Cumulative Review �� 32

Chapter 2

Basic Addition and Subtraction

Number Sense

2-1

Naming Numbers �� 36

2-2

Place Value �� 38

2-3

Millions �� 40

2-4

Comparing and Ordering Numbers �� 42

2-5

Rounding Numbers to the Tens or Hundreds Place �� 44

2-6

Rounding Large Numbers �� 46

2-7

Place Value with Money �� 48

2-8

Chapter Review �� 50

2-9

Cumulative Review �� 52

Level D

| TOC

| Lighthouse MATH

Addition

3-1

Adding Two-Digit Numbers �� 56

3-2

Adding Three-Digit Numbers �� 58

3-3

Adding Four-Digit Numbers �� 60

3-4

Adding Five-Digit Numbers �� 62

3-5

Column Addition �� 64

3-6

Estimating Sums �� 66

3-7

Adding Money �� 68

3-8

Addition Word Problems �� 70

3-9

Chapter Review �� 72

3-10

Cumulative Review �� 74

Chapter 4

Subtraction

4-1

Subtracting Two-Digit Numbers �� 78

4-2

Subtracting Three-Digit Numbers �� 80

4-3

Subtracting with Zeros �� 82

4-4

Subtracting Multi-Digit Numbers �� 84

4-5

Subtracting Across Zeros �� 86

4-6

Estimating Differences �� 88

4-7

Subtracting Money �� 90

4-8

Subtraction Word Problems �� 92

4-9

Chapter Review �� 94

4-10

Cumulative Review �� 96

Level D

| TOC

| Lighthouse MATH

Chapter 3

Chapter 5

5-1

Equal Groups and Arrays �� 100

5-2

Multiplication Facts 2 and 3 �� 102

5-3

Multiplication Facts 4 and 5 �� 104

5-4

Multiplication Facts 6 and 7 �� 106

5-5

Multiplication Facts 8 and 9 �� 108

5-6

Multiplication Facts 0, 1, and 10 �� 110

5-7

Multiplication Facts 11 and 12 �� 112

5-8

Chapter Review �� 114

5-9

Cumulative Review �� 116

Chapter 6

Multiplication Facts

Multiplying a Two- or Three-Digit Number

118

6-1

Multiplying by Multiples of 10, 100, and 1,000 �� 120

6-2

Multiplying Two Multiples of 10, 100, and 1,000 �� 122

6-3

Multiplying Two-Digit by One-Digit Numbers (No Regrouping) �� 124

6-4

Regrouping in Multiplication �� 126

6-5

Multiplying Two-Digit by One-Digit Numbers (With Regrouping) �� 128

6-6

Multiplying Three-Digit by One-Digit Numbers �� 130

6-7

More Multiplying Three-Digit by One-Digit Numbers �� 132

6-8

Multiplying Money �� 134

6-9

Chapter Review �� 136

6-10

Cumulative Review �� 138

Level D

| TOC

| Lighthouse MATH

Double-Digit Multiplication

140

7-1

Multiplying a Two-Digit or Three-Digit Number by a Multiple of Ten �� 142

7-2

Multiplying by Two-Digit Numbers �� 144

7-3

Multiplying by Two-Digit Numbers (With Regrouping) �� 146

7-4

Multiplying Three-Digit by Two-Digit Numbers (With Regrouping) �� 148

7-5

Estimating Products �� 150

7-6

Multiplication Word Problems �� 152

7-7

Chapter Review �� 154

7-8

Cumulative Review �� 156

Chapter 8

Division Facts and Rules

158

8-1

Introduction to Division �� 160

8-2

Dividing by Two and Three �� 162

8-3

Dividing by Four and Five �� 164

8-4

Dividing by Six and Seven �� 166

8-5

Dividing by Eight and Nine �� 168

8-6

Dividing by Zero and One �� 170

8-7

Multiplication and Division Fact Families �� 172

8-8

Solving Division with Multiplication �� 174

8-9

Dividing by Multiples of 10 �� 176

8-10

Equal Groups with Some Left Over �� 178

8-11

Divisibility Rules �� 180

8-12

Chapter Review �� 182

8-13

Cumulative Review �� 184

Level D

| TOC

| Lighthouse MATH

Chapter 7

Chapter 9

Long Division

186

9-1

Dividing with Remainders �� 188

9-2

Checking Division �� 190

9-3

Long Division �� 192

9-4

Long Division with Remainders �� 194

9-5

Understanding Remainders �� 196

9-6

Chapter Review �� 198

9-7

Cumulative Review �� 200

Chapter 10 Long Division (Continued) 10-1

Three-Digit Dividends �� 204

10-2

Three-Digit Dividends with Remainders �� 206

10-3

Zeros in Quotients �� 208

10-4

Three-Digit Dividends with Two-Digit Quotients �� 210

10-5

Dividing with Money �� 212

10-6

Four-Digit Dividends �� 214

10-7

Chapter Review �� 216

10-8

Cumulative Review �� 218

Chapter 11 Fractions

202

220

11-1

Introduction to Fractions �� 222

11-2

Equivalent Fractions �� 224

11-3

Finding Equivalent Fractions �� 226

11-4

Simplifying Fractions �� 228

11-5

Comparing Fractions on a Number Line �� 230

11-6

Comparing Fractions �� 232

11-7

Improper Fractions �� 234

11-8

Mixed Numbers �� 236

11-9

Comparing Mixed Numbers �� 238

11-10

Chapter Review �� 240

11-11

Cumulative Review �� 242

Level D

| TOC

| Lighthouse MATH

Chapter 12 Operations with Fractions

244

12-1

The Unit Fraction �� 246

12-2

Combining Fractions �� 248

12-3

Removing Fractions �� 250

12-4

Adding and Subtracting Fractions �� 252

12-5

Adding and Subtracting Mixed Numbers �� 254

12-6

Chapter Review �� 256

12-7

Cumulative Review �� 258

Chapter 13 Decimals

260

13-1

Tenths �� 262

13-2

Decimals with Whole Numbers �� 264

13-3

Hundredths �� 266

13-4

Comparing and Ordering Decimals �� 268

13-5

Chapter Review �� 270

13-6

Cumulative Review �� 272

274

14-1

Points, Lines, Line Segments, and Rays �� 276

14-2

Angles �� 278

14-3

Classifying Triangles �� 280

14-4

Classifying Quadrilaterals �� 282

14-5

Perimeter and Area �� 284

14-6

Understanding Time of Day �� 286

14-7

Inches, Feet, Yards, Miles �� 288

14-8

Cups, Pints, Quarts, Gallons �� 290

14-9

Ounces, Pounds, Tons �� 292

14-10

Dot Plots �� 294

14-11

Chapter Review �� 296

14-12

Cumulative Review �� 298

Level D

| TOC

| Lighthouse MATH

Chapter 14 Geometry, Measurement, and Data

C H A P T E R

In Chapter 1 we will practice

Basic Addition and Subtraction When two or more numbers are put together, we can use addition to find the total. When a number is taken away from another number, we can use subtraction to find what is left. • We will use addition to check subtraction. • We will use subtraction to check addition. • We will use rules to make adding and subtracting easier. • We will find patterns when we count. • We will skip count to find an amount of money.

1 - 1 | Addition and Subtraction Facts Write the number that comes next. DAILY REV IE W

L E A R N A ND C ONNEC T Addition and subtraction are opposites. When we add, we put two parts together to make a whole. When we subtract, we take one part away from the whole to find the part that is left.

Sam has 9 marbles, and Ron has 3 marbles. How many marbles do they have when they put them all together?

addend + addend =

sum

Ron takes his marbles back. How many marbles does Sam have now?

9 3 12

−

12 − 3 9

minuend − subtrahend = difference

AP P LY Solve. 1.

5 + 9

3 + 5

7 + 4

6 + 2

8 + 5

1 + 4

12 − 3

8 − 5

11 − 5

10.

4 − 1

11.

13 − 9

12.

12 − 3

Vocabulary Sum - the answer to an addition problem Difference - the answer to a subtraction problem Minuend - a number from which another is to be subtracted

Level D

Subtrahend - a number to be subtracted from another number Addend - a number added to another number

| Chapter 1 - 1

| Lighthouse MATH

Exercise | 1 - 1 Name

8 + 7

9 + 3

9 + 7

8 + 2

3 + 9

6 + 8

1 + 7

6 + 9

2 + 8

10.

8 + 7

11.

6 + 1

12.

9 + 4

13.

7 + 8

14.

2 + 7

15.

14 − 7

16.

8 − 3

17.

12 − 9

18.

10 − 7

19.

11 − 6

20.

16 − 7

21.

9 − 2

22.

11 − 4

23.

6 − 2

24.

11 − 8

25.

10 − 4

26.

13 − 7

27.

17 − 8

28.

8 − 7

29. 14 − 2 =

30. 9 + 3 =

31. 13 − 2 =

32. 7 − 2 =

33. 10 − 5 =

34. 6 + 5 =

35. 1 + 8 =

36. 9 − 4 =

37. 8 + 2 =

38. 11 − 2 =

39. 12 + 8 =

40. 18 − 4 =

Read the problem. Then solve. 41. Jody has 11 balloons. 3 balloons fly away. How many does she have now?

42. Gary walks 3 blocks east and 1 block south. How many blocks did he walk in all?

CH AL L ENGE Find the missing number. 43.

+ 9 = 13

44. 7 +

Level D

= 12

45. 11 −

| Chapter 1 - 1

| Lighthouse MATH

46. 19 −

Solve.

1 - 2 | Opposite Operations Solve. DAILY REV IE W

3+8=

15 − 7 =

L E A R N A ND C ONNEC T

9 6

−

We can check subtraction with addition. Start with your answer. Add the number you subtracted. 8

15 − 7

If you get the number you started with, your answer is correct.

18 − 7 =

1+2=3 3−2=1

Addition and subtraction are opposites. We can check addition with subtraction. Start with your answer. Subtract the number you added.

9+4=

If you get the number you started with, your answer is correct.

7 15

AP P LY

Add. Check by subtracting. 1.

11 5 + 6 11

−

3. 7 + 9

4. 4 + 7

−

7 + 8

−

11 − 3

Subtract. Check by adding. 5.

7 12 − 5 7

7. 15 − 7

Level D

| Chapter 1 - 2

8. 18 − 9

| Lighthouse MATH

Exercise | 1 - 2 Name

Add. Then, check your answer using subtraction. 1.

8 + 9

7 + 6

−

3 + 7

−

10 + 1

4 + 5

−

10.

1 + 4

−

2 + 3

12 + 2

−

11.

2 + 8

−

6 + 9

−

8 + 3

−

12.

4 + 9

−

16.

15 − 8

20.

18 − 7

24.

13 − 3

13.

16 − 8

17.

7 − 6

21.

10 − 6

14.

11 − 4

18.

14 − 5

22.

12 − 9

15.

12 − 4

19.

14 − 7

23.

7 − 5

Subtract. Then, check your answer using addition.

Solve. 25. Danny has 18 candies. He gives away 6 of them. How many does he have left?

26. Pete has $5. He gets $4 more for mowing the lawn. How much money does he have in total?

CH AL L ENGE A fact family is a group of 2 addition sentences and 2 subtraction sentences that have the same 3 numbers. 27. Write a fact family for the numbers 4, 5, and 9.

Level D

| Chapter 1 - 2

| Lighthouse MATH

1 - 3 | Rules of Addition and Subtraction Solve. DAILY REV IE W

3+8=

15 − 7 =

9+4=

18 − 7 =

L E A R N A ND C ONNEC T Addition and subtraction rules can help us find the sum or difference. Numbers can be added in any order.

3+5=8

Adding or subtracting zero does not change the number.

5+3=8

8+0=8

Subtracting a number from itself leaves zero.

Numbers cannot be subtracted in any order. 10 − 3 = 7

8−0=8

3 − 10 ≠ 7

8−8=0

AP P LY Add. 1.

6+2=

9+1=

5+7=

3+1=

6+7=

8+3=

1+9=

0+5=

Subtract. 9.

6−4=

13. 10 − 2 =

10. 7 − 1 =

11. 5 − 3 =

12. 9 − 3 =

14. 10 − 4 =

15. 10 − 7 =

16. 17 − 9 =

Level D

| Chapter 1 - 3

| Lighthouse MATH

Exercise | 1 - 3 Name

Subtract. 1.

6−6=

5−0=

9−9=

1−1=

2−0=

7−7=

10. 6 − 0 =

4−0=

5−5=

3−3=

11. 1 − 0 =

12. 8 − 8 =

Add in any order. 7 + 8

14.

6 + 0

15.

2 + 9

16.

6 + 5

17.

1 + 4

18.

0 + 9

19.

3 + 9

20.

1 + 4

21.

8 + 5

22.

0 + 7

23.

6 + 8

24.

2 + 6

25.

9 + 9

26.

6 + 3

27. 9 + 7 =

28. 2 + 7 =

29. 7 + 4 =

30. 8 + 8 =

31. 9 + 6 =

32. 1 + 8 =

33. 1 + 7 =

34. 1 + 5 =

35. 9 + 9 =

36. 6 + 7 =

37. 5 + 3 =

38. 5 + 5 = © Lighthouse Curriculum. Copying strictly prohibited.

13.

Read the problem. Then solve. 39. Tom spent $5 on the first day and $4 the next day. How much money did he spend?

40. On Monday, Fred walked 0 miles. On Wednesday, he walked 3 miles. How many miles did Fred walk altogether?

CH AL L ENGE Find the missing number. 41. 9 + 6 =

42. 6 +

Level D

| Chapter 1 - 3

+2=8+2+6

| Lighthouse MATH

1 - 4 | Column Addition Solve. 1.

DAILY REV IE W

8 + 2

7 + 1

9 + 0

3 − 2

9 − 5

11 − 8

L E A R N A ND C ONNEC T When you add 3 or more numbers you can choose which numbers to add first. You can pick the order of the numbers that makes adding easiest.

9 4 + 1 14

13 + 1 14

9 4 + 1 14

9 + 5 14

9 4 + 1 14

10 + 4 14

AP P LY Solve. 1.

4 3 + 2

3 0 + 2

1 3 + 6

4 5 + 1

2 1 + 1

4 4 + 2

1 5 + 3

1 3 + 2

3 3 + 1

10.

3 2 + 7

11.

0 5 + 2

12.

1 3 + 7

Level D

| Chapter 1 - 4

| Lighthouse MATH

Exercise | 1 - 4 Name

Solve. 1.

5 1 + 2

2 9 + 1

7 7 + 2

9 6 + 4

5 1 + 5

9 1 + 7

2 4 + 7

7 6 + 6

3 6 + 3

10.

8 7 + 2

11.

8 4 + 2

12.

6 4 + 6

13.

4 4 + 7

14.

3 8 + 5

15.

2 6 + 8

16.

7 6 + 9

17.

7 4 3 + 5

18.

8 1 5 + 4

19. 8 + 2 + 3 =

20. 6 + 1 + 4 =

21. 9 + 6 + 3 =

22. 7 + 2 + 2 =

23. 5 + 5 + 5 =

24. 9 + 7 + 1 =

25. 3 + 2 + 3 =

26. 3 + 8 + 7 =

27. 9 + 1 + 8 =

28. 5 + 3 + 2 =

29. 7 + 0 + 9 =

30. 2 + 5 + 2 = © Lighthouse Curriculum. Copying strictly prohibited.

Solve.

Read the problem. Then solve. 32. Frank has 6 toys, Eric has 9 toys, and Steven has 2 toys. How many toys do they have altogether?

31. There are 5 books on the yellow table, 3 books on the red table, and 6 books on the blue table. How many books are there in all?

CH AL L ENGE Solve. 33. 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 =

Level D

| Chapter 1 - 4

| Lighthouse MATH

1 - 5 | Counting by 1, 2, 3, and 4 Solve. 1.

4 2 + 3

DAILY REV IE W

7 8 + 5

5 5 + 5

6 2 + 4

5 1 + 5

4 7 + 3

L E A R N A ND C ONNEC T When we count by one, we say every number. When we skip count, we don’t say every number. To find the number that comes next, add the number you are skip counting by to the last number you counted. Skip counting by two: +2

Skip counting by three: +2

52, 54, 56, 58, 60 , 62

Skip counting by four: +3

60, 63, 66, 69, 72 , 75

+4 +4 +4 +4 +4

40, 44, 48, 52, 56 , 60

AP P LY Skip count by two. Write the next numbers. 1.

2, 4,

14, 16,

40, 42,

21, 24,

28, 32,

Skip count by three. Write the next numbers. 4.

3, 6,

12, 15,

Skip count by four. Write the next numbers. 7.

4, 8,

Level D

16, 20,

| Chapter 1 - 5

| Lighthouse MATH

Exercise | 1 - 5 Name

Count by one. Write the next numbers. 1.

97,

587,

498,

244,

699,

76,

952,

396,

789,

10. 897,

Skip count by two. Write the next numbers. 11. 78,

12. 56,

14. 128, 130, 132,

15. 526, 528,

13. 90,

16. 840, 842,

17. 3, 6,

18. 12, 15,

19. 21, 24,

22. 28, 32,

Skip count by three. Write the next numbers.

Skip count by four. Write the next numbers. 20. 4, 8,

21. 16, 20,

CH AL L ENGE Fill in the missing numbers. 23.

, 8,

, 16, 20,

Level D

| Chapter 1 - 5

| Lighthouse MATH

1 - 6 | Counting by 5, 10, 25, and 100

DAILY REV IE W

Skip count by four. Write the next numbers.

Skip count by two. Write the next numbers.

4, 8,

100, 102,

L E A R N A ND C ONNEC T When we skip count by 5, 10, 25, or 100, we can find a pattern. Remember that you can add the number you are skip counting by to the last number you counted to find the next number.

Skip counting by 5:

Skip counting by 10:

5, 10, 15, 20, 25, 30 , 35

10, 20, 30, 40, 50, 60 , 70

65, 70, 75, 80, 85, 90 , 95

126, 136, 146, 156, 166 , 176

Skip counting by 25:

Skip counting by 100:

25, 50, 75, 100

100, 200, 300, 400 , 500

200, 225, 250, 275, 300

385, 485, 585, 685 , 785

AP P LY Skip count by five. Write the next numbers. 1.

5, 10,

35, 40,

80, 85,

Skip count by ten. Write the next numbers. 4.

10, 20,

120, 130,

400, 410,

275, 300,

Skip count by 25. Write the next numbers. 7.

25, 50,

Level D

100, 125,

| Chapter 1 - 6

| Lighthouse MATH

Exercise | 1 - 6 Name

Skip count by five. Write the next numbers. 1.

65,

620, 625, 630,

45,

865, 870,

20,

440, 445,

360,

Skip count by ten. Write the next numbers. 7.

10. 26, 36, 46, 56,

11. 49, 59,

80,

140,

12. 337, 347,

13. 25,

14. 75, 100,

15. 600,

18. 499,

Skip count by 25. Write the next numbers.

Skip count by 100. Write the next numbers. 16. 156, 256,

17. 325,

CH AL L ENGE Fill in the missing numbers. 19.

, 75,

, 125, 150,

Level D

| Chapter 1 - 6

| Lighthouse MATH

1 - 7 | Counting Money

DAILY REV IE W

Skip count by 25. Write the next numbers.

Skip count by 100. Write the next numbers.

25,

584,

L E A R N A ND C ONNEC T We can use skip counting to find the value of a group of coins.

How much is each coin worth? Quarter 25 ¢ = $0.25

These are the coins Harry has in his pocket. How much money does he have? Nickel 5 ¢ = $0.05

25,

50,

75,

85,

Dime 10 ¢ = $0.10

Count by 25 and 10 to find how much money Harry has. Penny 1 ¢ = $0.01

Harry has 95 cents. We can write 95¢ or $0.95.

AP P LY Skip count to find how many cents. 1.

Vocabulary Quarter - a coin worth 25 cents

Dime - a coin worth 10 cents

Level D

Nickel - a coin worth 5 cents

| Chapter 1 - 7

| Lighthouse MATH

Penny - a coin worth 1 cent

Exercise | 1 - 7 Name

10.

Skip count to find how many cents.

CH AL L ENGE Danny has 4 coins that add up to 61 cents. Which coins are missing? 11.

Level D

| Chapter 1 - 7

| Lighthouse MATH

1 - 8 | Chapter Review Add. 1.

DAILY REV IE W

3 + 5

6 + 3

4 + 4

5 + 8

2 + 9

4 + 7

L E T ' S REV I EW Addition and Subtraction Are Opposites

Rules

We can check addition with subtraction. We can check subtraction with addition.

We can add in any order, but we must subtract in order.

9 + 7 = 16

16 − 7 = 9

2 + 8 = 10 8 + 2 = 10

7 + 9 = 16

16 − 9 = 7

10 − 8 = 2

Adding or subtracting 0 does not change a number.

Skip Counting

6+0=6

We can skip count by adding the same number again and again. Count by 2: Count by 3: Count by 4: Count by 5: Count by 10: Count by 25: Count by 100:

8 − 10 ≠ 2

6−0=6

Money

2, 4, 6, 8, 10,... 3, 6, 9, 12, 15,... 4, 8, 12, 16, 20,... 5, 10, 15, 20, 25,... 10, 20, 30, 40, 50,... 25, 50, 75, 100, 125,... 100, 200, 300, 400, 500,...

Penny 1 ¢ = $0.01

Dime 10 ¢ = $0.10

Nickel 5 ¢ = $0.05

Quarter 25 ¢ = $0.25

AP P LY Solve. 1.

12 − 8

7 + 2

10 − 8

9 − 5

13 − 4

8 + 7

5 2 + 7

4 9 + 3

2 9 + 4

10.

3 2 + 1

11.

9 8 + 7

12.

7 6 + 9

Level D

| Chapter 1 - 8

| Lighthouse MATH

Exercise | 1 - 8 Name

Solve. 1.

0+7=

1+8+2=

9+0=

4−0=

9+3=

5+8=

5+1=

10 + 4 =

10. 9 + 3 =

1+9+4=

Skip count by five. Write the next numbers.

Skip count by ten. Write the next numbers.

11. 85,

12. 38,

Skip count by 25. Write the next numbers.

Skip count by 100. Write the next numbers.

13. 100,

14. 228,

15.

16.

17.

18.

19.

20.

Level D

| Chapter 1 - 8

| Lighthouse MATH

Skip count to find how many cents.

1 - 9 | Cumulative Review

Solve. 1.

8 + 6

14 − 8

5 − 2

7 + 6

11 − 3

7 + 7

3 + 3

2 + 3

5 + 3

10.

7 + 9

11.

8 + 3

12.

9 − 8

13.

1 + 9

14.

1 + 4

15.

11 − 9

16.

5 + 1

17.

2 + 5

18.

6 + 4

19.

1 + 3

20.

3 + 8

21.

14 − 7

22.

2 − 1

23.

11 − 8

24.

9 − 6

25.

17 − 9

26.

9 + 9

27.

10 − 9

28.

13 − 5

29.

17 − 8

30.

8 + 9

31.

9 − 1

32.

7 + 8

33.

4 + 7

34.

16 − 8

35.

5 + 4

36.

5 + 7

37.

5 − 1

38.

10 − 1

39.

12 − 8

40.

12 − 7

41.

7 + 5

42.

9 + 3

43.

4 + 5

44.

15 − 7

45.

2 + 9

46.

9 + 5

47.

8 − 6

48.

2 + 4

49.

3 + 1

50.

15 − 9

51.

5 + 5

52.

5 − 3

53.

8 + 8

54.

4 − 1

55.

15 − 8

56.

16 − 7

57.

16 − 5

58.

2 + 8

59.

7 − 2

60.

9 + 8

61.

8 − 4

62.

19 − 4

63.

14 − 4

Level D

| Chapter 1 - 9

| Lighthouse MATH

Exercise | 1 - 9 Name

Add. 1.

1 + 7

7 + 8

3 + 4

5 + 4

4 + 4

8 + 2

5 + 5

3 + 6

1 + 5

10.

4 + 2

11.

6 + 3

12.

4 + 7

13.

2 + 4

14.

3 + 9

15.

2 + 6

16.

6 + 2

17.

5 + 6

18.

9 + 8

19.

1 + 9

20.

9 + 6

21.

2 + 3

Subtract. 7 − 5

23.

6 − 4

24.

14 − 6

25.

12 − 9

26.

11 − 4

27.

3 − 1

28.

9 − 7

29.

18 − 9

30.

17 − 9

31.

8 − 3

32.

4 − 2

33.

15 − 8

34.

13 − 4

35.

3 − 2

36.

13 − 6

37.

12 − 8

38.

7 − 1

39.

13 − 7

40.

8 − 6

41.

11 − 2

42.

11 − 5

22.

Skip count by two. Write the next numbers. 43. 34, 36,

44. 492, 494,

Skip count by four. Write the next numbers. 45. 4, 8,

46. 16, 20,

Skip count by five. Write the next numbers. 47. 10, 15,

48. 100, 105,

Level D

| Chapter 1 - 9

| Lighthouse MATH

2 C H A P T E R

In Chapter 2 we will practice

Number Sense Understanding how the number system works makes doing math easier. The place value system tells us how much each digit is worth. • We will understand each place value as being 10 times greater than the one to the right of it. • We will use commas to separate groups of three digits in large numbers. • We will compare numbers. • We will round numbers. • We will write money amounts using a decimal point and place value.

2 - 1 | Naming Numbers Solve. 1.

DAILY REV IE W

8 + 4

7 + 9

19 − 11

18 − 7

5 + 8

16 − 12

L E A R N A ND C ONNEC T Digits are the numbers 0 - 9. Some numbers have 1 digit, and some have many digits.

Hundreds

Tens

Ones

4 hundreds

2 tens

5 ones

Four hundred

twenty

five

425 has 3 digits. We can put each digit in a place value chart. We say “four hundred twenty-five.”

AP P LY Name the number. Write the missing word.

Hundreds

Tens

Ones

three hundred 3.

-two

Hundreds

Tens

Ones

One hundred eighty-

Hundreds

Tens

Ones

Nine

fifteen

Hundreds

Tens

Ones

Four

Hundreds

Tens

Ones

hundred seven

forty

Hundreds

Tens

Ones

hundred twenty-six

Vocabulary Digits - the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 Place value chart - a chart that shows the value of each digit Standard form - a number written with digits Word form - a number written in words

Level D

| Chapter 2 - 1

| Lighthouse MATH

Exercise | 2 - 1 Name

Write each number. 1.

nine hundred thirty-one

seven hundred fifty-nine

six hundred forty-two

five hundred twenty-six

four hundred sixty

eight hundred seventeen

two hundred seventy-six

one hundred seventy-one

nine hundred sixty-two

10. three hundred fifty-four

11. five hundred thirty-one

12. six hundred ninety-three

13. four hundred seventy-five

14. eight hundred thirty-six

15. two hundred forty

16. one hundred eighty-two

Name the numbers. Write the missing words. 17. 900

hundred

18. 239

two hundred

-nine

19. 308

hundred

20. 892

eight hundred

22. 585

five

two

twenty-

eighty-

21. 222

Read the problem. Then solve. 23. The fair gave away five hundred eighteen stuffed bears. How many stuffed bears were given away?

24. Rebecca plants nine hundred eightyseven seeds in her garden. How many seeds does she plant?

CH AL L ENGE 25. The zoo has one thousand, three hundred fifty-nine animals. How many animals do they have?

Level D

| Chapter 2 - 1

| Lighthouse MATH

2 - 2 | Place Value Write each number. DAILY REV IE W

four hundred twenty-one

seven hundred thirty-five

nine hundred two

six hundred twenty-nine

L E A R N A ND C ONNEC T We can show big numbers on the place value chart. We always put a comma between the hundreds and the thousands places. The number 523,612 has 6 digits. Each digit has its own place on the chart. The place of the digit tells us its value or how much it is worth.

523,612 Place

Hundred thousands

Ten thousands

Thousands

Hundreds

Tens

Ones

Digit

Value

500,000

20,000

3,000

600

five hundred twenty-three thousand, six hundred twelve

AP P LY Fill in the missing numbers in the place value chart. 767,859

1. Place

Hundred thousands

Thousands

Digit Value

Ten thousands

Hundreds

700,000

7,000

5 800

Vocabulary Digits - the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 Value - how much something is worth Place value chart - a chart that shows the value of each digit

Level D

| Chapter 2 - 2

Tens

| Lighthouse MATH

Ones

Exercise | 2 - 2 Name

Find the digit. 1.

489,635

hich digit is in the ones W place?

124,342

Which digit is in the ten thousands place?

386,199

Which digit is in the hundreds place?

984,312

Which digit is in the hundred thousands place?

997,343

Which digit is in the tens place?

739,217

Which digit is in the thousands place?

276,120

Which digit is in the hundreds place?

196,354

Which digit is in the ten thousands place?

983,491

Which digit is in the ten thousands place?

10.

529,334

Which digit is in the hundred thousands place?

11.

396,256

Which digit is in the ones place?

12.

715,032

Which digit is in the hundreds place?

13. What is the value of the digit 5?

14. What is the value of the digit 9?

15. What is the value of the digit 3?

16. What is the value of the digit 8?

17. What is the value of the digit 1?

18. What is the value of the digit 6?

There are 596,183 different flowers at the local market. Find the value of the digits.

CH AL L ENGE Solve. 19. The numbers 80 and 800 both have the digit 8 in them. How many times greater is the 8 in 800 than 80?

Level D

| Chapter 2 - 2

| Lighthouse MATH

2 - 3 | Millions Find the digit. 1.

DAILY REV IE W

389,421 2.

Which digit is in the ones place?

Which digit is in the thousands place?

Which digit is in the hundred thousands place?

L E A R N A ND C ONNEC T In the year 2020, 331,449,281 people lived in the United States. This number has 9 digits and reaches the hundred millions place. We always put a comma after the millions and the thousands places.

331,449,281 Place

Hundred Millions

Digit

Value

Ten Millions Millions

300,000,000 30,000,000 1,000,000

Hundred thousands

Ten thousands

Thousands

400,000

40,000

9,000

200

Hundreds Tens Ones

three hundred thirty-one million, four hundred forty-nine thousand, two hundred eighty-one

AP P LY Fill in the missing numbers in the place value chart. 497,345,685

1. Place

Hundred Millions

Millions

Digit Value

Ten Millions

400,000,000

Hundred thousands

, 7,000,000

Level D

Ten Thousands , Hundreds Tens Ones thousands

300,000

| Chapter 2 - 3

, ,

| Lighthouse MATH

5 600

Exercise | 2 - 3 Name

Write the number. 1. eight hundred sixteen million, seven hundred thirty-two thousand, nine hundred seventy-five 2. one million, nine hundred seventy-three thousand, eight hundred forty-two 3. sixteen million, eight hundred twenty-four thousand, three hundred fifty-seven 4. two hundred forty-three million, two hundred fifty-eight thousand, six hundred seventy-nine 5. seven hundred fifteen million, six hundred forty-three thousand, two hundred fifty-seven 6. twenty-two million, thirty-eight thousand, five hundred twenty-one Write the value of the underlined digit. 7. 1,236,608

8. 16,529,873

10. 951,876,923

11. 614,574,321

12. 21,022,583

13. 3,519,329

14. 3,392,302

15. 348,930,067

16. 48,412,497

17. 332,745,019

18. 431,697,842

38,241,573

CH AL L ENGE Write this number in word form. 19. 312,420,392

Level D

| Chapter 2 - 3

| Lighthouse MATH

2 - 4 | Comparing and Ordering Numbers Write the value of the underlined digit. 1.

DAILY REV IE W

8,622,957

295,615,921

347,736,855

L E A R N A ND C ONNEC T In 2020, 21,538,187 people lived in Florida, and 20,201,249 people lived in New York. Which state had more people? To compare and order numbers, we compare the digits from left to right. Line up the numbers by place value.

First, compare the digits in the highest place value.

If they are the same, move to the right until you find digits that are different. Then, compare them.

21,538,187 20,201,249

2=2

1>0

More people lived in Florida than in New York because 21,538,187 > 20,201,249. © Lighthouse Curriculum. Copying strictly prohibited.

Write > for more than. Write < for less than.

We can write the numbers in order from least to greatest: 20,201,249; 21,538,187

AP P LY Compare. Write > or < in the circle. 1.

549

544

4,576

4,676

773

394

393

6,748

6,747

4,524

Write the numbers in order from least to greatest. 7.

4,874; 5,452; 4,982

492; 214; 491

Level D

| Chapter 2 - 4

| Lighthouse MATH

673

4,538

Exercise | 2 - 4 Name

Compare. Write > or < in the circle. 1.

385

185

972,915

200

200,000

643

618

816

3,982,931

10. 726

276

11. 643,890

3,478

3,487

800

799

3,972,931

204

402

642,890

12. 9,296

972,951

642

9,286

Write the numbers in order from least to greatest. ,

14. 582,374; 538,724; 583,274

15. 2,630; 2,130; 2,430

16. 241; 214; 421

17. 5,824; 6,842; 8,524; 5,648

Read the problem. Then solve. 18. Amy has 3,462 beads. Jessica has 3,409 beads. Who has more beads?

19. A bakery sells 452 cookies on Monday and 398 cookies on Tuesday. On which day do they sell fewer cookies?

CH AL L ENGE 20. The Mississippi River is 2,340 miles long. The Missouri River is 2,341 miles long. The Potomac River is 405 miles long. List the rivers in order from shortest to longest.

Level D

| Chapter 2 - 4

| Lighthouse MATH

13. 8,250; 8,249; 8,256

2 - 5 | Rounding Numbers to the Tens or Hundreds Place Write the numbers in order from least to greatest. 1. 351; 153; 513

DAILY REV IE W

2. 426; 246; 624 ,

3. 7,841; 1,847; 4,718

L E A R N A ND C ONNEC T Numbers that end in zero are easier to use.

To round to the nearest ten, find the closest number that ends in a zero. To round to the nearest hundred, find the closest number that ends in two zeros. Underline the place you want to round to.

Look at the digit to the right of that place.

To the nearest ten

526

To the nearest hundred

526

526 500 510 520 530 540 550 560 570 580 590 600

the nearest hundred

the nearest ten

Follow the rules for rounding.

The digits to the right of the underlined digit turn to 0.

4 or lower: Round down. The underlined digit stays the same.

530

5 or higher: Round up. Add 1 to the underlined digit.

500

AP P LY Round each number to the nearest ten and hundred. 1.

373 Round to the nearest ten: Round to the nearest hundred:

415 Round to the nearest ten: Round to the nearest hundred:

Vocabulary The nearest ten - the closest number that ends in a zero The nearest hundred - the closest number that ends in two zeros

Level D

| Chapter 2 - 5

| Lighthouse MATH

Exercise | 2 - 5 Name

Round each number to the nearest ten. 1.

10. 19

11. 236

12. 181

13. 375

14. 758

15. 317

16. 729

17. 151

18. 567

19. 826

20. 354

21. 398

22. 888

23. 609

24. 120

25. 562

26. 456

27. 846

28. 535

29. 736

30. 150

31. 745

32. 212

33. 850

34. 499

35. 758

Round each number to the nearest hundred.

CH AL L ENGE Read the problem. Then solve. 36. The Levine family is saving for their summer vacation. Each night at the rental costs $559, and they will stay for six nights. About how much should the Levines save?

Level D

| Chapter 2 - 5

| Lighthouse MATH

2 - 6 | Rounding Large Numbers Round each number to the nearest ten. 1. 286

DAILY REV IE W

2. 88

3. 762

4. 12

5. 349

L E A R N A ND C ONNEC T We can follow rules to round numbers to any place value. Mark the place you are rounding.

8,538,223

Look to the right of that digit.

Use the rules for rounding.

Change the rest of the digits to zero.

8,538,223

4 or lower: Marked digit stays the same 5 or higher: Marked digit goes up

9,000,000

Let's see how the numbers change when we round 8,538,223 to different places. Millions

Hundred Thousands

Ten Thousands

Thousands

8,538,223 9,000,000

8,538,223 8,500,000

8,538,223 8,540,000

8,538,223 8,538,000

AP P LY Round each number to the highest place value. 1.

9,327

56,572

432

294,256

9,425,295

25,978

2,573

552,784

4,444,444

Level D

| Chapter 2 - 6

| Lighthouse MATH

Exercise | 2 - 6 Name

Round each number to the nearest million. 1.

1,698,308

6,394,873

4,598,345

8,467,920

7,934,885

9,504,669

4,505,689

7,432,333

Round each number to the nearest hundred thousand. 9.

689,321

10. 5,789,354

11. 1,348,902

12. 9,321,302

13. 632,981

14. 7,389,115

15. 673,922

16. 3,328,399

17. 69,327

18. 845,632

19. 962,835

20. 8,927,124

21. 6,735,893

22. 1,989,999

23. 556,932

24. 9,294,312 © Lighthouse Curriculum. Copying strictly prohibited.

Round each number to the nearest ten thousand.

Round each number to the nearest thousand. 25. 4,592

26. 932,674

27. 3,492,850

28. 9,764,920

CH AL L ENGE 29. The distance from Earth to the sun is 91,843,000 miles. The teacher said the distance is about 91,800,000 miles. What place did she round it to?

Level D

| Chapter 2 - 6

| Lighthouse MATH

2 - 7 | Place Value with Money Round each number to the nearest hundred thousand. 1. 893,524

DAILY REV IE W

2. 594,269

3. 918,259

4. 258,519

L E A R N A ND C ONNEC T Money also has place value. Dollars and cents are separated by a decimal. We always write two digits for the cents. How much money does Steven have? Dollars

Cents

decimal point

Write a dollar sign and then the number of dollars.

Write a decimal point next to the dollars.

Write the number of cents.

$2.

$2.38

AP P LY Count the money. Write each amount. 1.

Level D

| Chapter 2 - 7

| Lighthouse MATH

Steven has $2.38. We say, "two dollars and thirty-eight cents."

Exercise | 2 - 7 Name

Count the money. Write each amount. 1.

Write each amount. 6. 5 dollars, 5 dimes, and 6 pennies

$ 8. 1 dollar and 6 cents

11. 2 dollars and 4 dimes

13. 2 dollars and 6 dimes $

15. 5 dollars and 97 cents

10. 3 dollars and 64 cents $

12. 6 dimes and 7 pennies

$ 14. 6 dollars and 8 dimes

9. 8 dimes and 9 cents

7. 4 dollars and 44 cents

5. 8 dollars, 5 dimes, and 2 pennies

16. twelve dollars and 15 pennies $

CH AL L ENGE 17. Henry is buying flowers for his mother. They cost $4.25. He didn’t have any dollar bills. What is one way that he could have paid?

Level D

| Chapter 2 - 7

| Lighthouse MATH

2 - 8 | Chapter Review Write the amount of money. 1. 8 dollars, 3 dimes, and 6 pennies

DAILY REV IE W

2. 24 cents

3. 6 dollars and 4 pennies

L E T ' S REV I EW We can tell a digit’s value by where it is placed in the number.

984,312,645 Place

Hundred Millions

Ten Millions

Millions

Digit

Value

900,000,000

300,000

10,000

2,000

600

80,000,000 4,000,000

Hundred Ten Thousands , thousands thousands

To compare numbers, start comparing the digits in the highest place value and then move to the right. 3,456,329

To round numbers:

3,739,246

3=3 4<7 © Lighthouse Curriculum. Copying strictly prohibited.

Hundreds Tens Ones

3,456,329 < 3,739,246

Mark a digit.

Look to the right.

Round down or round up.

49,345

50,000

AP P LY Find the digit in each place. 1.

923,495

Which digit is in the ones place?

21,654

Which digit is in the ten thousands place?

512,798

Which digit is in the hundreds place?

154,876

Which digit is in the hundred thousands place?

45,312

Which digit is in the thousands place?

593,296

Which digit is in the tens place?

Level D

| Chapter 2 - 8

| Lighthouse MATH

Exercise | 2 - 8 Name

Compare. Write > or < in the circle. 1.

492

494

384,329

400

4,000

679

384,536

479

56,392

2,345,567

55,295

2,345,569

Round each number to the nearest ten. 7.

10. 18

11. 48

12. 46

13. 92

14. 56

15. 699

16. 588

17. 677

18. 847

19. 458

20. 312

21. 923

22. 759

23. 4,549

24. 8,946

25. 22,338

26. 58,717

27. 1,152

28. 7,211

29. 42,584

30. 64,475 © Lighthouse Curriculum. Copying strictly prohibited.

Round each number to the nearest thousand.

Write each amount. 31. 5 dollars and 46 cents

32. 7 dollars and 29 cents

$ 34.

33. 9 dollars and 4 dimes

35.

36.

Level D

| Chapter 2 - 8

| Lighthouse MATH

2 - 9 | Cumulative Review

Solve. 1.

6 + 8

5 + 9

1 + 3

9 − 7

12 − 5

14 − 6

16 − 8

12 − 8

3 + 9

10.

5 + 8

11.

6 + 1

12.

16 − 7

13.

1 + 9

14.

9 + 7

15.

4 + 4

16.

9 + 2

17.

12 − 6

18.

5 + 1

19.

12 − 9

20.

11 − 4

21.

12 − 4

22.

9 − 4

23.

10 − 4

24.

17 − 9

25.

15 − 9

26.

6 − 3

27.

8 − 5

28.

3 + 7

29.

8 − 1

30.

4 + 5

31.

17 − 8

32.

8 + 2

33.

1 + 2

34.

10 − 3

35.

7 + 5

36.

1 + 4

37.

7 − 3

38.

6 − 5

39.

9 − 8

40.

6 + 9

41.

15 − 7

42.

11 − 5

43.

1 + 8

44.

3 − 2

45.

8 + 6

46.

10 − 7

47.

4 + 3

48.

9 + 4

49.

7 + 7

50.

3 + 8

51.

3 + 4

52.

7 + 6

53.

3 + 6

54.

6 − 2

55.

7 − 6

56.

3 + 3

57.

8 + 2

58.

6 + 8

59.

9 + 3

60.

4 + 11

61.

9 − 3

62.

13 − 5

63.

4 + 2

Level D

| Chapter 2 - 9

| Lighthouse MATH

Exercise | 2 - 9 Name

Add. 1.

2 + 8

8 + 5

6 + 8

3 + 1

4 + 2

3 + 2

1 + 2

1 + 9

7 + 8

10.

6 + 3

11.

3 + 8

12.

3 + 6

13.

9 + 8

14.

8 + 3

15.

3 + 5

16.

8 + 7

17.

8 + 1

18.

3 + 7

19.

8 + 9

20.

2 + 1

21.

2 + 6

Subtract. 6 − 1

23.

12 − 5

24.

5 − 4

25.

9 − 3

26.

7 − 6

27.

10 − 6

28.

11 − 8

29.

13 − 4

30.

12 − 7

31.

9 − 4

32.

13 − 6

33.

9 − 2

34.

10 − 3

35.

3 − 2

36.

15 − 6

37.

11 − 3

38.

15 − 8

39.

9 − 1

40.

10 − 5

41.

6 − 4

42.

8 − 7

22.

Skip count to find how many cents. 43.

44.

45.

46.

47.

48.

Level D

| Chapter 2 - 9

| Lighthouse MATH

3 C H A P T E R

In Chapter 3 we will practice

Addition In this chapter, we will be adding multidigit numbers. When adding large numbers, it is important to keep your work organized. • We will add numbers by lining up their place values and working from right to left. • We will regroup when the sum in any place is greater than 9. • We will estimate sums by rounding to easier numbers. • We will add money amounts. • We will apply what we have learned to solve real-world problems.

3 - 1 | Adding Two-Digit Numbers Add. 1.

DAILY REV IE W

9 + 6

8 + 2

1 + 7

7 + 9

3 + 4

8 + 5

L E A R N A ND C ONNEC T When adding, we line up the place values and add one place at a time. If the sum in any place is more than 9, we need to regroup. Break the answer into tens and ones. Write the number of ones as the answer. Carry the tens to the place to the left. Line up the place values. 58 + 64 Hundreds

Tens

5 6

Ones

Add the ones. Regroup if needed.

Add the tens. Regroup if needed.

8 + 4 = 12 Carry the 1.

1 + 5 + 6 = 12 Carry the 1.

Hundreds

Tens

Ones

8 4

8 4 2

5 6

Hundreds

Tens

Ones

5 6 2

+ 1

8 4 2

AP P LY Solve. 1.

43 + 5 Tens

Ones

Tens

39 + 42 Ones

95 + 76 Hundreds

Tens

Ones

Vocabulary Place value - the value of a digit based on its position

Level D

Regrouping - trading place value units without changing the number’s value

| Chapter 3 - 1

| Lighthouse MATH

Exercise | 3 - 1 Name

Add. 1.

56 + 72

25 + 34

28 + 3

87 + 94

67 + 22

68 + 29

96 + 38

82 + 5

93 + 14

10.

25 + 34

11.

76 + 98

12.

44 + 21

13.

33 + 29

14.

97 + 65

15.

31 + 82

16.

76 + 6

17.

48 + 54

18.

31 + 67

Rewrite the problem and add. 19. 14 + 99

20. 49 + 73

21. 83 + 7

22. 27 + 34

23. 64 + 34

24. 53 + 8

25. 83 + 92

26. 85 + 64

27. Ann counts 35 butterflies on her walk on Monday and 62 butterflies on her walk on Tuesday. How many butterflies does she see in all?

28. Victor reads 86 pages in the morning and 95 pages at night. How many pages does he read in all?

CH AL L ENGE Can you solve these problems in your head? 29. 49 + 27 =

30. 67 + 45 =

Level D

| Chapter 3 - 1

31. 51 + 39 =

| Lighthouse MATH

Read the problem. Then solve.

3 - 2 | Adding Three-Digit Numbers Add. 1.

DAILY REV IE W

38 + 43

67 + 15

33 + 4

42 + 11

79 + 34

12 + 53

L E A R N A ND C ONNEC T One gumball machine has 674 gumballs, and the other has 579 gumballs. How many gumballs are there altogether?

To find the total, add and .

Line up the place values.

Add the ones. Regroup if needed.

674 + 579

674 + 579 3

Add the tens. Regroup if needed.

Add the hundreds. Regroup if needed.

1 1

1 1 1

674 + 579 1,253

674 + 579 53

There are 1,253 gumballs.

AP P LY Solve. 1.

2. 5 6 4 + 2 3

3. 4 6 2 + 1 9 4

Level D

4. 6 3 9 + 2 4 3

| Chapter 3 - 2

5. 9 4 8 + 3 4 4

| Lighthouse MATH

1 8 3 + 8 4 7

Exercise | 3 - 2 Name

Add. 1.

143 + 36

278 + 5

187 + 194

697 + 22

458 + 632

983 + 221

271 + 39

431 + 135

224 + 311

10.

362 + 695

11.

252 + 186

12.

335 + 972

13.

392 + 136

14.

921 + 8

15.

456 + 929

16.

238 + 496

17.

745 + 397

18.

294 + 673

Tip!

Rewrite the problem and add. 19. 782 + 47

20. 320 + 377

21. 444 + 649

Make sure to line up ones on top of ones and tens on top of tens. 324 + 21

22. 784 + 26

23. 683 + 563

24. 284 + 114

25. 293 + 63

324 21 +

26. 515 + 28

28. 210 students returned their permission slips for a class trip. The next day, 39 more students brought in their slips. How many brought permission slips in all?

27. Justin drove 345 miles on Monday and 134 miles on Tuesday. How many miles did he drive altogether?

CH AL L ENGE Find the missing addend.

29.

4 8 7 + 1, 2 3 4

Level D

| Chapter 3 - 2

| Lighthouse MATH

Read the problem. Then solve.

3 - 3 | Adding Four-Digit Numbers Add. 1.

DAILY REV IE W

467 + 231

377 + 120

521 + 304

409 + 6

392 + 199

147 + 285

L E A R N A ND C ONNEC T There are 1,206 maple trees and 2,085 fir trees. How many trees are there altogether? To find the total number of trees, add and . Line up the place values.

Add the ones. Regroup if needed.

2,085 + 1,206

2,085 + 1,206 1

Add the tens. Regroup if needed.

2,085 + 1,206 91

Add the hundreds. Regroup if needed.

Add the thousands. Regroup if needed.

2,085 + 1,206 291

2,085 + 1,206 3,291

There are 3,291 trees altogether.

AP P LY Solve. 1.

2. 1, 2 0 8 + 4 0 3

5, 6 2 4 + 2, 3 1 0

6. 2, 2 1 4 + 5 4 5

4. 4, 3 2 1 + 7, 8 1 3

7. 6, 7 7 5 + 4, 5 0 0

Level D

| Chapter 3 - 3

5, 9 8 1 + 8, 4 2 5

8. 8, 9 0 9 + 2, 8 1 0

| Lighthouse MATH

3, 6 9 9 + 5 6 3

Exercise | 3 - 3 Name

Add. 1.

3,998 + 4,503

8,165 + 4,872

3,426 + 8,246

5,216 + 4,412

3,378 + 2,195

5,558 + 4,123

1,412 + 3,301

1,116 + 4,799

9,668 + 4,303

10.

8,217 + 7,403

11.

4,588 + 6,735

12.

7,111 + 5,623

13.

6,607 + 59

14.

1,218 + 4,733

15.

6,788 503

Rewrite the problem and add. 16. 1,782 + 407

17. 2,650 + 4,700

18. 4,568 + 4,568

19. 7,205 + 7,900

20. 1,299 + 4,799

21. 1,200 + 487

22. 5,000 + 7,966

23. 2,765 + 4,761

25. A cookie factory bakes 2,550 cookies on Monday and 1,345 cookies on Tuesday. How many cookies do they bake in all?

24. One box has 1,245 paper clips. Another box has 3,456 paper clips. How many paper clips are in both boxes?

CH AL L ENGE Add.

26.

5,356 8,873 + 7,470

Level D

27.

2,068 8,476 + 6,855

| Chapter 3 - 3

| Lighthouse MATH

Read the problem. Then solve.

3 - 4 | Adding Five-Digit Numbers Add. 1.

DAILY REV IE W

3,721 + 7,557

5,638 + 6,147

1,135 + 233

4,319 + 8,754

6,499 + 6,005

L E A R N A ND C ONNEC T Last year, Helen traveled 13,550 miles. This year, she has traveled 16,575 miles. How many total miles has she traveled? To find the total distance Helen has traveled, add and . Add the ones. Regroup if needed.

Add the tens. Regroup if needed.

13,550 + 16,575 5

13,550 + 16,575 25

Add the hundreds. Regroup if needed. 1 1

13,550 + 16,575 125

Add the thousands. Regroup if needed.

Add the ten thousands. Regroup if needed.

13,550 + 16,575 30,125

13,550 + 16,575 0,125

Helen has traveled 30,125 miles.

AP P LY Solve. 1.

2. 5 4, 6 7 8 + 4 5, 6 7 0

1 2, 3 0 0 + 5, 5 4 0

6. 1 0, 9 5 0 + 9, 0 3 4

4. 1 1, 1 0 4 + 4 2, 0 3 6

7. 6 1, 3 3 1 + 6 2, 9 8 7

Level D

| Chapter 3 - 4

1 0, 2 9 0 + 1 4, 0 3 2

8. 7 0, 3 0 4 + 8 4, 0 3 0

| Lighthouse MATH

6 5, 9 9 9 + 5 0, 5 5 0

Exercise | 3 - 4 Name

Add. 1.

45,975 + 54,351

74,500 + 50,239

34,119 + 5,230

99,140 + 45,229

89,998 + 15,784

63,145 + 4,999

53,678 + 22,000

88,100 + 44,332

50,600 + 26,110

10.

34,558 + 25,770

11.

97,348 + 5,770

12.

60,987 + 14,352

13.

11,990 + 32,457

14.

66,614 + 25,632

15.

18,008 + 21,240

Rewrite the problem and add. 16. 11,582 + 40,709

17. 17,625 + 2,407

18. 21,793 + 40,798

19. 64,322 + 1,629

20. 55,001 + 98,119

21. 50,302 + 5,669

23. The aquarium has 10,700 fish in a large tank and 5,600 fish in a small tank. How many fish are there in all?

22. A factory makes 12,435 lightbulbs in one week and the same amount the next week. How many lightbulbs does it make altogether?

CH AL L ENGE Find the missing digits.

24. +

, 2 , 8 7, 6 5 0,

Level D

| Chapter 3 - 4

| Lighthouse MATH

Read the problem. Then solve.

3 - 5 | Column Addition Add. 1.

DAILY REV IE W

13,605 + 24,550

25,549 + 25,459

46,137 + 5,400

37,137 + 24,354

55,171 + 45,632

L E A R N A ND C ONNEC T The 4th grade collects coins in 3 jars. The first jar has 156 coins, the second jar has 639 coins, and the last jar has 798 coins. How many coins are there altogether? To find the total amount of coins, we add

, and

When adding numbers in a column, add any two digits at a time and then add the sum to the next digit. Add the ones. Regroup if needed.

Add the tens. Regroup if needed.

156 639 + 798 3

Add the hundreds. Regroup if needed.

156 639 + 798 1,593

156 639 + 798 93

15 + 8 23

There are 1,593 coins altogether.

AP P LY Solve. 1.

5 3 9 6 2 2

3. 2 9 9 1 1 5 + 1 7 8

Level D

| Chapter 3 - 5

5 3 7 4 3 5

5. 3 6 7 9 7 + 3 5 7

| Lighthouse MATH

1 0 0 9 8 + 2 0 5

Exercise | 3 - 5 Name

Add. 1.

55 90 + 28

32 65 + 15

48 70 + 17

68 30 + 21

136 45 + 220

503 60 + 80

43 45 + 42

302 75 + 165

87 104 + 28

10.

18 22 + 75

11.

354 69 + 104

12.

48 36 + 21

13.

580 740 + 220

14.

145 75 + 225

15.

470 810 + 252

16.

798 652 + 145

17.

745 765 + 725

18.

890 960 + 450

19. 43 + 89 + 23

20. 13 + 65 + 14

21. 87 + 26 + 32

22. 50 + 74 + 35

23. 451 + 784 + 220

24. 42 + 196 + 202

25. 456 + 142 + 222

26. 430 + 841 + 120

Read the problem. Then solve. 27. A factory makes 125 toys on Monday, 275 toys on Tuesday, and 130 toys on Wednesday. How many toys did it make in all?

28. A grocery store orders 50 cans of soup, 25 cans of fruit, and 55 cans of vegetables. What is the total number of cans ordered?

CH AL L ENGE Add.

29. 5,692 + 658 + 8,631 + 25 + 9 + 582 =

Level D

| Chapter 3 - 5

| Lighthouse MATH

Rewrite and add.

3 - 6 | Estimating Sums Add. 1. DAILY REV IE W

22 85 + 102

422 105 + 75

202 65 + 550

654 84 + 510

575 99 + 145

230 109 + 525

L E A R N A ND C ONNEC T Aquarium A has 1,235 gallons of water. Aquarium B has 1,950 gallons of water. About how many gallons of water are in both aquariums? We don’t need to find the exact answer. To estimate the number of gallons of water, round and to the nearest hundred and add. Round the 1st number.

Round the 2nd number.

1,235 + 1,950

1,200

1,200 2,000

Add. 1,235 + 1,950

1,200 + 2,000 3,200

Together, the aquariums have about 3,200 gallons of water.

AP P LY Round to the nearest ten and then estimate. 1.

53 + 25

425 + 63

78 + 11 6.

713 + 649

Vocabulary Estimate - find an answer that is close but not exact Round - change a number to the nearest ten, hundred, or thousand so that it is easier to work with

Level D

| Chapter 3 - 6

63 + 27

| Lighthouse MATH

6,543 + 6,301

81 + 49

Exercise | 3 - 6 Name

Round to the nearest ten to estimate the answer.

Tip! When the digit to the right is… …4 or less, round down. …5 or more, round up.

48 + 69

44 + 26

87 + 32

48 + 92

22 + 56

11 + 86

Round to the nearest hundred to estimate the answer. 7.

411 + 623

784 + 215

3,279 + 4,622

12.

5,212 + 1,833

Round to the highest place value to estimate the answer. 10.

11.

67 + 28

484 + 221

Read the problem. Estimate to find the answer. 13. There are 22 girls in Mrs. Taylor’s classroom and 19 girls in Mrs. Smith’s classroom. About how many girls are there altogether?

14. There are 98 photos in one photo album and 253 photos in another. About how many photos are there altogether?

CH AL L ENGE Which estimate is more accurate? Why? 15. A.

3,509 + 2,614

4,000 + 3,000 7,000

Level D

3,509 + 2,614

3,500 + 2,600 6,100

| Chapter 3 - 6

| Lighthouse MATH

3 - 7 | Adding Money Round to the highest place value and then solve. 1.

DAILY REV IE W

26 + 49

126 + 357

5,209 + 6,525

L E A R N A ND C ONNEC T Josh spent $5.89 on shampoo and $3.79 on soap. How much money did he spend altogether? To find the total amount of money, add $ and $ . Line up the decimal points.

Start adding from the right. Regroup if needed. Move left to the next place value and repeat. 1

$5.89 + $3.79

1 1

$5.89 + $3.79 8

Bring the decimal down and write the dollar sign.

1 1

$5.89 + $3.79 68

$5.89 + $3.79 9 68

1 1

$5.89 + $3.79 $9.68

Josh spent $9.68 altogether.

AP P LY Add. 1.

2. $ 4 . 1 9 $ 6 . 2 9

+ $

6. $ 4 6 . 9 9 + $ 7 4 . 1 3 .

$ 1 9 . 8 9 + $ 2 6 . 1 1 $ .

4. $ 3 . 2 5 + + $ 5 . 5 0 $ .

7. +

$ 6 . 7 4 $ 0 . 7 1 $

Level D

| Chapter 3 - 7

$ 2 4 . 6 6 + $ 4 5 . 2 2 $ . 8.

$ 2 2 . 8 7 + $ 1 7 . 0 5 $ .

| Lighthouse MATH

$ 8 . 0 1 $ 1 . 0 9 $

Exercise | 3 - 7 Name

Add. 1.

$4.25 + $3.50

$1.10 + $7.85

$5.60 + $2.15

$0.75 + $8.20

$6.42 + $1.25

$45.67 + $12.32

$88.10 + $14.95

$23.50 + $71.85

$64.29 + $35.71

10.

$9.99 + $92.50

11.

$99.49 $28.43 + $15.87

12.

$18.45 $69.02 + $11.86

13.

$24.24 $9.12 + $33.34

14.

$10.85 $14.97 + $3.90

15.

$5.08 $31.55 + $8.92

16. $4.45 + $5.55

17. $6.35 + $5.59

18. $2.18 + $1.90

19. $1.39 + $3.12

20. $3.98 + $0.84

21. $1.34 + $6.49

Rewrite and then add.

Read the problem. Then solve. 23. Frank buys a mug for $2.50 and a pitcher for $12.84. How much does he spend in all?

22. Jack buys a pair of socks for $2.30. He also buys a pair of gloves for $5.50. How much money does he spend?

CH AL L ENGE Write the money amount with the dollar sign. 24. How much money is 6 quarters, 3 dimes, and 8 pennies?

Level D

| Chapter 3 - 7

| Lighthouse MATH

3 - 8 | Addition Word Problems Add. 1.

DAILY REV IE W

$24.44 + $11.05

$105.44 + $560.12

$15.00 + $7.50

$5.05 + $2.89

$5.99 + $2.99

L E A R N A ND C ONNEC T On Monday, 1,256 people shopped at the market. On Tuesday, 3,545 people shopped at the market. How many people shopped altogether? We need to find the number of people who shopped on Monday and Tuesday and add them together.

How many people shopped on Monday? How many people shopped on Tuesday?

1,256 3,545 4,801

Altogether, 4,801 people shopped on Monday and Tuesday.

AP P LY Read the problem. Then solve. 1. The Alpine family drove 433 miles yesterday and 389 miles today. How many total miles did they drive?

2. Moses used 650 pounds of mulch and 325 pounds of stone. What is the total weight of the materials?

3. The library has 1,840 fiction books and 2,450 non-fiction books. How many books does the library have?

4. George pays $875 to fix his car and $1,100 for new tires. How much does he spend?

Level D

| Chapter 3 - 8

| Lighthouse MATH

Exercise | 3 - 8 Name

Read the problem. Then solve. 2. Mickey picked 5,300 oranges on Monday, and Paul picked 2,950 oranges the same day. How many oranges were picked on Monday?

3. The school ordered 4,800 pencils in October and 2,710 in November. How many total pencils did they order?

4. A baker baked 55 cookies in the morning and 120 cookies in the afternoon. How many cookies did she bake?

5. A tulip farm planted 1,400 tulips last year. This year they planted 2,500 tulips. How many tulips were planted in both years?

6. A plane flew 2,750 miles and then flew another 3,200 miles. How many miles did the plane fly in all?

7. The Madison family picked 52 apples and 38 peaches. How many pieces of fruit did they pick in all?

8. Mr. Brown drove 1,152 miles in May and 1,825 miles in June. How many miles did he drive these two months?

9. Adam already has $1,254 in his bank account. He adds $3,105 to his account. How much money is in his account?

10. There are 1,250 seats in the wedding hall, and 875 more seats are added. How many people can the hall seat?

1. One section of the school library has 895 books. Another section has 756 books. How many books do the two sections have together?

CH AL L ENGE Read the problem. Then solve. 11. The grocery store stocked a total of 4,285 cans last month. They stock 5,629 cans this month. They plan to stock 5,206 cans next month. How many cans will they have stocked in all three months?

Level D

| Chapter 3 - 8

| Lighthouse MATH

3 - 9 | Chapter Review Add. 1.

DAILY REV IE W

14 + 7

23 + 9

27 + 13

92 + 5

88 + 9

37 + 4

L E T ' S REV I EW Adding Numbers Line up the place values and add from right to left. Regroup if needed. 1

1,206 + 2,085 3,291

768 439 + 915 2,122

When adding numbers in a column, add two digits at a time and then add the sum to the next digit.

17 + 5 22

Estimating Sums

Adding Money

Round both numbers, then add.

Line the numbers up by the decimal points and add from right to left. Bring down the decimal and add the dollar sign. 1 1

1,235 + 1,950

1,200 + 2,000 3,200

$3.29 + $3.79 $7.08

AP P LY Add. 1.

39 + 45

42 + 67

33 + 9

97 + 18

23 + 87

25 + 99

322 + 21

983 + 122

443 + 264

10.

308 + 194

11.

416 + 291

12.

409 + 321

Level D

| Chapter 3 - 9

| Lighthouse MATH

Exercise | 3 - 9 Name

Add. 1.

2,345 + 1,934

3,798 + 4,978

3,087 + 26

4,905 + 9,348

9,394 + 229

39,265 + 8,532

74,298 + 33,000

44,200 + 38,965

35,705 + 37,399

10.

99,294 + 13,476

11.

$5.25 + $2.50

12.

$3.14 + $7.24

13.

$2.45 + $3.19

14.

$0.82 + $7.69

15.

$6.24 + $2.39

16.

49 36 + 31

17.

854 25 + 292

18.

33 275 + 51

19.

49 37 + 51

20.

529 33 + 299

Round to the nearest ten to estimate the answer. 38 + 46

22.

23.

75 + 48

84 + 56

24.

34 + 29

21.

Read the problem. Then solve. 25. The Monroe family saved $4,000 last year and $5,000 this year. How much do they have saved altogether?

26. The school library checked out 356 books in October and 942 books in November. How many books did they check out in total?

27. A gardener planted 165 roses last year and 482 roses this year. How many roses did the gardener plant altogether?

28. The Green family traveled 3,800 miles last year and 4,550 miles this year. How many total miles did they travel?

Level D

| Chapter 3 - 9

| Lighthouse MATH

3 - 10 | Cumulative Review

Solve. 1.

11 − 3

2 + 6

18 − 9

2 + 9

3 + 7

12 − 7

8 + 4

7 + 7

6 − 5

10.

8 + 5

11.

14 − 6

12.

7 + 6

13.

1 + 1

14.

3 − 1

15.

12 − 4

16.

8 − 2

17.

4 − 2

18.

3 + 8

19.

14 − 5

20.

8 − 3

21.

8 + 7

22.

8 − 1

23.

3 + 5

24.

8 + 8

25.

11 − 9

26.

1 + 2

27.

13 − 6

28.

6 + 5

29.

14 − 9

30.

10 − 9

31.

12 − 3

32.

4 + 1

33.

15 − 8

34.

10 − 2

35.

1 + 8

36.

8 − 6

37.

7 + 9

38.

9 − 3

39.

7 − 6

40.

2 + 2

41.

7 + 3

42.

7 − 5

43.

14 − 7

44.

7 + 1

45.

9 − 1

46.

9 − 5

47.

5 + 6

48.

7 + 8

49.

6 + 4

50.

9 − 4

51.

10 − 4

52.

8 + 3

53.

3 − 2

54.

9 + 6

55.

4 + 8

56.

3 + 9

57.

12 − 5

58.

16 − 8

59.

9 + 1

60.

5 − 2

61.

12 + 4

62.

8 + 3

63.

5 + 11

Level D

| Chapter 3 - 10

| Lighthouse MATH

Exercise | 3 - 10 Name

Add. 1.

271 + 631

471 + 501

648 + 251

307 + 368

285 + 465

643 + 249

8,440 + 1,047

1,718 + 2,412

7,552 + 1,227

10.

1,825 + 2,010

11.

5,084 + 2,057

12.

1,363 + 1,816

Subtract. 6 − 2

14.

9 − 5

15.

17 − 8

16.

5 − 4

17.

12 − 6

18.

12 − 4

19.

11 − 5

20.

9 − 4

21.

8 − 3

22.

10 − 6

23.

8 − 2

24.

17 − 9

25.

7 − 3

26.

11 − 4

27.

10 − 5

28.

16 − 8

29.

15 − 8

30.

12 − 3

31.

18 − 9

32.

10 − 9

33.

5 − 3

13.

Find the digit. 34. 348,962

Which digit is in the ones place?

35.

492,115

Which digit is in the ten thousands place?

36. 471,203

Which digit is in the hundreds place?

37.

884,298

Which digit is in the hundred thousands place?

Find the value of each digit in the number 356,789. 38. What is the value of the digit 7?

39. What is the value of the digit 3?

40. What is the value of the digit 6?

41. What is the value of the digit 8?

Level D

| Chapter 3 - 10

| Lighthouse MATH

4 C H A P T E R

In Chapter 4 we will practice

Subtraction In this chapter, we will be subtracting 2-, 3-, 4-, and 5-digit numbers. When subtracting large numbers, it is important to keep your work organized. • We will subtract numbers by lining up their place values and working from right to left. • We will regroup and borrow when the top digit in any place is smaller than the bottom digit. • We will estimate differences by rounding to easier numbers. • We will subtract money amounts. • We will apply what we have learned to solve real-world problems.

4 - 1 | Subtracting Two-Digit Numbers Subtract. 1.

DAILY REV IE W

9 − 2

2 − 1

8 − 3

7 − 7

4 − 0

6 − 5

L E A R N A ND C ONNEC T When subtracting, line up the place values and subtract one place at a time. If the top digit is less than the bottom digit, borrow from the place value to the left. When borrowing, regroup 1 ten for 10 ones. Take away 1 from the tens and add 10 to the ones.

Line up the place values. 53 − 27 Tens

5 2

−

Subtract the ones. 7 cannot be subtracted from 3. Regroup. Borrow a ten: 5 − 1 = 4 tens Give it to the ones: 3 + 10 = 13 ones

Ones

3 7

Tens

Ones

Tens

Ones

5 2

−

Subtract the tens.

3 7

5 2

−

3 7

AP P LY Write the problem in the place value chart. Fill in the missing numbers. 1.

92 − 37 Tens

Ones

Tens

−

65 − 29 Ones

−

Level D

| Chapter 4 - 1

73 − 8 Tens

−

| Lighthouse MATH

Ones

Exercise | 4 - 1 Name

Subtract. 1.

45 − 12

52 − 18

73 − 4

67 − 35

61 − 35

85 − 57

40 − 2

58 − 27

90 − 1

10.

34 − 19

11.

55 − 8

12.

77 − 16

13.

82 − 47

14.

41 − 6

15.

95 − 47

16.

68 − 3

17.

40 − 16

18.

82 − 55

19.

79 − 4

20.

51 − 28

21.

37 − 12

22.

72 − 11

23.

61 − 5

24.

85 − 32

25.

63 − 27

26.

90 − 44

27.

58 − 6

28.

42 − 25

Rewrite and subtract. 29. 88 − 36

30. 93 − 6

31. 54 − 39

32. 38 − 20

33. 87 − 9

34. 56 − 23

35. George earned $24 this week, but he spent $18. How much money does he have now?

36. Ruth read 16 pages of the 45 pages that were assigned to her. How many more pages does she have left to read?

CH AL L ENGE Find the missing number. 37.

8 7 −

38.

3 5 −

4 5

Level D

| Chapter 4 - 1

| Lighthouse MATH

Read the problem. Then solve.

4 - 2 | Subtracting Three-Digit Numbers Subtract. 1.

DAILY REV IE W

74 − 28

86 − 54

91 − 33

69 − 47

45 − 26

L E A R N A ND C ONNEC T The Monroe family is driving 416 miles to visit their grandparents. If they stop for lunch after 218 miles, how many more miles do they have left to drive? To find the number of miles they have left, subtract from .

Line up the place values. Put the bigger number on top.

416 − 218

Subtract the tens. Regroup if needed.

Subtract the ones. Regroup if needed.

Subtract the hundreds.

0 16

10 3 0 16

416 − 218 8

416 − 218 98

416 − 218 198

They still need to drive 198 miles.

AP P LY Fill in the missing numbers. 1.

2. 9 3 2 − 5 6

3. 3 7 6 − 9

Level D

4. 5 2 8 − 7 9

| Chapter 4 - 2

5. 6 8 1 − 2 9 3

| Lighthouse MATH

8 1 4 − 3 2 7

Exercise | 4 - 2 Name

Subtract. 1.

897 − 56

435 − 124

782 − 50

395 − 182

678 − 2

546 − 325

257 − 13

654 − 231

899 − 356

10.

529 − 27

11.

731 − 448

12.

692 − 9

13.

529 − 142

14.

532 − 14

15.

814 − 503

16.

436 − 102

17.

427 − 9

18.

863 − 541

19.

315 − 198

20.

527 − 314

21.

643 − 25

22.

832 − 438

23.

961 − 5

24.

415 − 196

Rewrite and subtract. 25. 789 − 47

26. 612 − 235

27. 932 − 7

28. 358 − 129

29. 536 − 18

30. David earned $622 this week, and he spent $455. How much money does he have now?

Read the problem. Then solve. 31. Judy has 794 beads, and she uses 315 of them for a project. How many beads does she have left?

CH AL L ENGE Find the missing number. 32. 564 −

= 333

Level D

| Chapter 4 - 2

| Lighthouse MATH

4 - 3 | Subtracting with Zeros Subtract. 1.

DAILY REV IE W

143 − 68

514 − 126

921 − 455

156 − 79

842 − 367

932 − 458

L E A R N A ND C ONNEC T Remember:

Sometimes, there is a 0 in the top number. If we need to borrow from it, we move left to the next place value until we find a number we can borrow from.

Line up the place values. 503 − 267

Regroup to subtract the ones. There are not enough tens to regroup. Borrow a hundred: 5 − 1 = 4 0 + 10 = 10 Borrow a ten: 10 − 1 = 9 3 + 10 = 13 4 10

503 − 267

1,000 = 10 hundreds 1 hundred = 10 tens 1 ten = 10 ones

503 − 267

Subtract the tens.

Subtract the hundreds.

9 4 10 13

4 9 13

503 − 267

503 − 267 6

503 − 267 36

503 − 267 236

AP P LY Fill in the missing numbers. 1.

2. 4 0 2 − 1 5 6

3. 6 0 5 − 2 3 8

Level D

4. 8 0 1 − 4 4 3

| Chapter 4 - 3

5 3 0 7 − 1 1 9

| Lighthouse MATH

9 0 4 − 5 2 7

Exercise | 4 - 3 Name

Subtract. 1.

405 − 126

702 − 345

502 − 243

807 − 568

901 − 438

305 − 188

601 − 325

508 − 299

903 − 417

10.

804 − 615

11.

207 − 79

12.

306 − 128

13.

607 − 459

14.

405 − 156

15.

401 − 233

16.

107 − 49

17.

905 − 827

18.

506 − 407

19.

704 − 256

20.

904 − 479

21.

301 − 185

22.

603 − 216

23.

403 − 267

24.

802 − 534

Rewrite and subtract. 26. 501 − 322

27. 908 − 849

28. 403 − 107

Read the problem. Then solve. 29. A baker starts the morning with 603 cookies. By lunch, she has sold 348 cookies. How many cookies are left?

30. A route is 402 miles long. If a truck has already driven 165 miles, how many more miles must the truck drive?

CH AL L ENGE Subtract. 31. 1,008 − 649 =

Level D

| Chapter 4 - 3

| Lighthouse MATH

25. 703 − 418

4 - 4 | Subtracting Multi-Digit Numbers Subtract. 1.

DAILY REV IE W

602 − 345

804 − 629

406 − 189

205 − 158

903 − 427

L E A R N A ND C ONNEC T A group of hikers is climbing a mountain that is 9,245 feet tall. They have climbed 4,568 feet. How many more feet until they reach the top? To find how much further they need to climb, subtract from . Line up the place values. 9,245 − 4,568

Regroup to subtract the ones.

Regroup to subtract the tens.

Regroup to subtract the hundreds.

3 15

13 1 3 15

11 13 8 1 3 15

9,245 − 4,568 7

9,245 − 4,568 77

9,245 − 4,568 677

Regroup to subtract the thousands. 11 13 8 1 3 15

9,245 − 4,568 4,677

They need to climb 4,677 more feet.

AP P LY Fill in the missing numbers. 1.

2. 5, 2 3 4 − 1, 6 5 5

8, 1 1 2 − 4 5 6

6. 8, 1 2 4 − 5, 3 4 6

4. 6, 4 2 1 − 2, 7 8 5

7. 2, 7 9 1 − 1, 8 3 5

Level D

| Chapter 4 - 4

9, 3 4 2 − 5, 8 6 7

8. 6, 3 5 2 − 2, 4 6 5

| Lighthouse MATH

−

6, 7 2 1 9 8 7

Exercise | 4 - 4 Name

Subtract. 1.

54,321 − 12,543

5,432 − 1,675

6,324 − 1,548

9,114 − 4,326

51,342 − 24,563

8,211 − 3,456

42,156 − 18,367

12,431 − 5,652

87,423 − 38,545

10.

4,512 − 2,634

11.

73,145 − 45,267

12.

12,345 − 8,456

13.

9,233 − 5,455

14.

61,234 − 25,456

15.

21,342 − 12,563

16.

5,621 − 1,735

17.

95,123 − 67,234

18.

84,112 − 36,225

19.

4,321 − 1,432

20.

7,314 − 2,545

Rewrite and subtract. 22. 52,431 − 8,654

23. 43,125 − 26,437

Read the problem. Then solve. 25. There are 14,532 pine trees in the forest. A logging company cut down 9,645 trees. How many trees are now in the forest?

24. A truck driver wants to drive 91,225 miles this year. He has already driven 82,341 miles. How many more miles until he reaches his goal?

CH AL L ENGE Subtract. 26. $254,312 − $164,425 =

Level D

| Chapter 4 - 4

| Lighthouse MATH

21. 7,312 − 4,586

4 - 5 | Subtracting Across Zeros Subtract. 1.

DAILY REV IE W

7,899 − 5,965

23,451 − 17,985

45,015 − 26,785

12,985 − 6,989

67,855 − 35,897

L E A R N A ND C ONNEC T There were 4,000 balloons at a carnival. A strong wind made 634 balloons float away. How many balloons are left? To find how many balloons are left, subtract Line up the place values.

4,000 − 634

Subtract the ones. Regroup one place value at a time.

from

Subtract the tens.

9 9 3 10 1010

4,000 − 634 6

4,000 − 634 66

. Subtract the hundreds.

−

Subtract the thousands.

9 9 3 10 1010

4,000 634 366

4,000 − 634 3,366

There are 3,366 balloons left.

AP P LY Fill in the missing numbers. 1.

2. 6, 0 0 5 − 1, 4 3 2

2, 0 0 0 − 8 6 7

5 0, 3 0 2 − 1 4, 2 7 5

5. 1 0, 0 0 0 − 6, 3 4 1

6. 8 0, 0 1 5 − 2 3, 6 4 1

Level D

| Chapter 4 - 5

| Lighthouse MATH

3, 0 0 0 − 1, 2 5 4

Exercise | 4 - 5 Name

Subtract. 1.

5,005 − 1,245

2,025 1,432

8,500 − 3,672

6,030 − 2,891

1,060 − 456

9,080 − 5,128

43,001 − 15,624

29,200 − 7,431

76,000 − 32,845

10.

60,130 − 28,154

11.

10,000 − 4,327

12.

90,000 − 45,671

13.

30,000 − 12,589

14.

100,000 − 45,231

15.

16.

7,000 − 3,114

17.

20,000 − 5,432

18.

5,000 − 2,341

19.

10,000 − 7,428

20.

−

4,000 2,637

40,000 − 16,532

Rewrite and subtract. 22. 6,000 − 4,213

23. 91,030 − 54,681

Read the problem. Then solve. 24. The Smiths have $50,000 in the bank. They spend $32,416. How much money do they have left?

25. A large hall has 20,105 seats. 8,132 seats are filled. How many seats are empty?

CH AL L ENGE Subtract. 26. 100,000 − 43,275 =

Level D

| Chapter 4 - 5

| Lighthouse MATH

21. 80,109 − 32,175

4 - 6 | Estimating Differences Subtract. 1.

DAILY REV IE W

5,000 − 2,684

10,000 − 4,372

60,000 − 15,247

8,000 − 3,115

30,000 − 12,981

L E A R N A ND C ONNEC T Ben is reading a book that is 892 pages long. He has read 317 pages so far. About how many pages does Ben have left to read? We don’t need to find the exact answer. To estimate the number of pages Ben has left to read, round 892 and 317 to the nearest hundred and subtract. Round the first number. 892 − 317

Round the second number.

900

−

892 317

900 300

Subtract. 892 − 317

−

900 300 600

Ben has about 600 pages left to read.

AP P LY Round to the highest place value to estimate the difference. 1.

87 − 45

367 − 72

−

63 − 36

1,086 − 825

Level D

| Chapter 4 - 6

−

| Lighthouse MATH

928 − 167

−

1,789 − 950

−

Exercise | 4 - 6 Name

Round to the nearest ten to estimate the answer. 1.

52 − 12

−

463 − 113

−

51 − 45

1,876 − 245

−

6,125 − 847

−

12.

4,873 − 675

−

Round to the nearest hundred to estimate the answer. 4.

920 − 432

−

654 − 127

−

Round to the nearest thousand to estimate the answer. 7.

2,345 − 1,389

−

2,005 − 1,116

−

Round to the highest place value to estimate the answer. 10.

8,412 − 625

−

11.

651 − 475

−

Read the problem. Then solve. 14. David wants to run a total of 2,800 miles this year. He has run 1,125 miles so far. About how many more miles does he need to run?

13. Last month, 8,245 people visited the park. This month, 1,890 people visited. About how many more people visited last month than this month?

CH AL L ENGE Round to the nearest hundred to estimate the difference. 15. Two food trucks are selling food. Truck A started with 1,200 sandwiches and has 392 sandwiches left. Truck B started with 1,500 sandwiches and has 618 sandwiches left. Which truck sold more sandwiches?

Level D

| Chapter 4 - 6

| Lighthouse MATH

4 - 7 | Subtracting Money Subtract. 1.

DAILY REV IE W

5,003 − 1,289

3,004 − 1,945

3,800 − 1,745

5,040 − 2,243

1,060 − 456

L E A R N A ND C ONNEC T Gary goes to the store with $10.25. He buys a snack for $6.75. How much money does he have left? To find the remaining money, subtract $ from $ . Line up the decimal points.

$10.25 − $6.75

Bring the decimal down. Write the dollar sign.

Start subtracting from the right. Regroup if needed. Move left to the next place value and repeat.

$10.25 − $6.75 0

9 0 10 12

0 9 12

$10.25 − $6.75 50

$10.25 − $6.75 3 50

$10.25 − $6.75 $3.50

Gary has $3.50 left.

AP P LY Fill in the missing numbers. 1.

$ 2 5 4. 8 2 − $ 1 3 7 .4 5 $ .

$ 6 2 4. 5 1 − $ 2 8 1 . 3 6 $ .

Level D

$ 4 5 6 . 1 9 − $ 1 2 8 .0 5 $ .

$ 9 3 8 . 1 5 − $ 4 7 2 . 6 4 $ .

| Chapter 4 - 7

| Lighthouse MATH

$ 1, 5 8 2 . 6 4 − $ 7 4 1 . 3 8 $ .

$ 7 5 1 .4 8 − $ 2 6 3 . 2 9 $ .

Exercise | 4 - 7 Name

Subtract. 1.

$85.42 − $32.19

$542.81 − $264.50

$94.15 − $47.60

$826.34 − $549.18

$72.63 − $18.45

$61.28 − $25.50

$942.15 − $678.09

$53.74 − $26.81

$734.56 − $ 382.71

10.

$42.10 − $15.35

11.

$90.55 − $42.78

12.

$850.44 − $362.52

13.

$38.22 − $19.45

14.

$427.61 − $159.28

15.

$76.31 − $ 28.14

16.

$516.32 − $284.15

17.

$933.47 − $566.21

18.

$145.20 − $62.75

19.

$742.19 − $485.05

20.

$238.56 − $149.20

Rewrite and subtract. 21. $472.19 − $285.45

22. $815.22 − $647.38

23. $614.33 − $352.68

Read the problem. Then solve. 25. Howard is saving for a new bike that costs $825.99. He has saved $548.50. How much more money does he need to buy the bike?

24. Abe has $452.60 in his bank account. After spending $187.45 on groceries, how much money is in his bank account?

CH AL L ENGE Subtract. 26. $1,245.15 − $687.58 =

Level D

| Chapter 4 - 7

| Lighthouse MATH

4 - 8 | Subtraction Word Problems Subtract. 1.

DAILY REV IE W

$82.41 − $36.59

$124.15 − $98.26

$56.02 − $17.45

$213.11 − $85.64

$100.00 − $42.35

L E A R N A ND C ONNEC T Eitan has a goal to run 1,500 miles. By the end of the winter, he has run 862 miles. How many more miles does he need to reach his goal? We need to subtract the number of miles Eitan ran from his goal. 14 9 0 4 1010

How many miles is Eitan’s goal?

1,500 − 862 638

How many miles has he already run?

Eitan has 638 miles to go until he reaches his goal.

AP P LY Solve. 1. The school library had 24,312 books on the shelves. 1,845 books were ruined or lost this school year. How many books does the library have left?

2. In two days, the Morris family drove 1,420 miles. If they drove 675 miles on Day 1, how many miles did they drive on Day 2?

,045 people lived in Elmwood last 8 year. This year only 6,158 people live there. How many more people lived in Elmwood last year?

Level D

| Chapter 4 - 8

1 2,405 birds are flying south. 3,826 of them fly over the ocean, and the rest fly over the land. How many birds fly over the land?

| Lighthouse MATH

Exercise | 4 - 8 Name

1. There are 45,000 parking spaces at the zoo. If 38,215 of them are taken, how many are still empty?

2. Building 1A is 828 yards tall. Building 1B is 330 yards tall. How much taller is Building 1A than Building 1B?

3. A ship is carrying 12,450 containers. It unloads 3,575 containers. How many containers are still on the ship?

4. A giant oak tree is 2,200 years old. A nearby pine tree is 145 years old. What is the difference in their ages?

5. The Miller family is driving 2,880 miles from New York to Los Angeles. They have already traveled 1,929 miles. How many more miles do they need to drive?

6. A factory made 9,005 chocolate bars. They found 218 that could not be sold. How many are ready to be sold?

7. A mountain climber is at a height of 6,112 feet. The top of the mountain is 14,505 feet high. How many more feet until the climber reaches the top?

8. A bookstore has 1,342 copies of the newest book. They sell 85 copies the first week. How many copies are left?

9. The trail at the park is 15,300 feet long. A group of hikers already walked 6,425 feet. How many more feet until they walk the whole trail?

10. Molly has collected 225 seashells. Sara has collected 150 seashells. How many more seashells does Molly have than Sara?

Solve.

CH AL L ENGE Solve. 11. A rocket weighs 1,200,000 pounds at launch. After the first stage, it separates, and now it weighs only 350,000 pounds. How much weight did it lose?

Level D

| Chapter 4 - 8

| Lighthouse MATH

4 - 9 | Chapter Review Subtract. 1.

DAILY REV IE W

22 − 14

38 − 24

82 − 3

94 − 78

58 − 35

73 − 19

L E T ' S REV I EW Subtracting Numbers Line up the place values and subtract from right to left. Regroup if needed. A.

11 13 8 1 3 15

4 15

55 − 27 28

9 9 3 101010

9,245 − 4,568 4,677

4,000 − 634 3,366

Estimating Differences

Subtracting Money

Round both numbers, then subtract.

Line the numbers up by the decimal points and subtract from right to left. Bring down the decimal and add the dollar sign.

2 14

3,445 − 1,721

0 12 12

3,400 − 1,700 1,700

$13.25 − $4.35 $8.90

AP P LY Subtract. 1.

392 − 29

229 − 148

987 − 90

495 − 335

596 − 4

321 − 188

308 − 124

701 − 345

805 − 338

10.

607 − 487

11.

502 − 413

12.

109 − 18

Level D

| Chapter 4 - 9

| Lighthouse MATH

Exercise | 4 - 9 Name

Subtract. 1.

35,392 − 22,975

3,948 − 2,389

7,942 − 4,958

6,008 − 3,897

3,076 2,345

6,700 − 4,984

11.

5,000 − 1,289

12.

70,000 − 9,792

13.

9,000 − 3,986

14.

−

7,194 5,648

39,956 − 16,398

−

9,030 3,564

10.

4,009 − 456

30,000 − 9,497

15.

60,000 − 29,783

Round to the highest place value to estimate the answer. 16.

17.

3,900 − 1,435 2,465

18.

4,451 − 2,173 2,278

6,856 − 499 6,357

Subtract. $67.48 − $21.67

20.

$364.81 − $256.57

21.

$56.83 − $13.95

22.

$795.34 − $272.94

23.

$41.65 − $18.79

Read the problem. Then solve. 24. A hall seats 35,000 people. If 27,345 people are seated, how many seats are empty?

25. A bridge is 398 feet tall. A building nearby is 492 feet tall. How much taller is the building than the bridge?

26. A truck is carrying 29,007 boxes. At the first stop, it unloads 4,933 boxes. How many boxes are still on the truck?

27. A giant tree is 1,000 years old. Another tree is 396 years old. What is the difference in their ages?

Level D

| Chapter 4 - 9

| Lighthouse MATH

19.

4 - 10 | Cumulative Review

Solve. 1.

12 − 6

4 + 1

6 − 1

2 + 6

6 + 1

5 + 8

15 − 9

4 + 7

7 + 4

10.

11 − 4

11.

12 − 8

12.

3 + 8

13.

8 + 6

14.

2 + 5

15.

6 + 4

16.

10 − 6

17.

9 + 4

18.

4 − 3

19.

2 + 9

20.

4 + 2

21.

12 − 4

22.

13 − 9

23.

16 − 9

24.

15 − 7

25.

13 − 7

26.

8 + 1

27.

5 − 2

28.

7 + 6

29.

9 + 8

30.

5 + 2

31.

7 − 1

32.

3 + 5

33.

11 − 8

34.

11 − 9

35.

3 + 1

36.

3 + 6

37.

6 + 3

38.

8 − 7

39.

6 + 7

40.

10 − 2

41.

7 + 3

42.

9 − 1

43.

1 + 1

44.

5 + 7

45.

7 − 4

46.

10 − 3

47.

9 − 5

48.

3 + 2

49.

6 + 6

50.

2 + 1

51.

1 + 5

52.

1 + 3

53.

6 − 5

54.

16 − 8

55.

7 − 3

56.

5 + 9

57.

8 + 2

58.

5 + 3

59.

11 + 5

60.

12 − 4

61.

17 − 5

62.

9 − 5

63.

6 + 8

Level D

| Chapter 4 - 10

| Lighthouse MATH

Exercise | 4 - 10 Name

Add. 1.

330 + 285

790 + 501

967 + 546

199 + 402

898 + 553

864 + 312

8,225 + 4,505

5,862 + 1,395

4,228 + 2,924

10.

6,076 + 1,454

11.

5,355 + 8,567

12.

3,982 + 1,958

13.

560 − 445

14.

682 − 330

15.

510 − 83

16.

830 − 268

17.

859 − 581

18.

707 − 354

19.

9,311 − 8,184

20.

9,298 − 3,435

21.

4,887 − 1,705

22.

6,571 − 1,599

23.

6,566 − 4,564

24.

7,150 − 3,779

Add. 25.

5 9 + 2

26.

3 4 + 1

27.

1 5 + 2

28.

8 7 + 1

29.

4 5 + 6

30.

2 9 + 8

31.

23 45 + 81

32.

89 22 + 19

33.

31 48 + 39

34.

439 27 + 118

35.

907 30 + 80

36.

531 29 + 333

Level D

| Chapter 4 - 10

| Lighthouse MATH

Subtract.

5 C H A P T E R

In Chapter 5 we will practice

Multiplication Facts Multiplication is repeated addition. When many equal groups are added together, we can find the total by multiplying. • We will use arrays to model multiplication facts. • We will use skip counting to solve multiplication facts. • We will use doubles to solve multiplication facts. • We will use tricks to solve multiplication facts.

5 - 1 | Equal Groups and Arrays Add. DAILY REV IE W

3+3+3=

8+8+8+8=

6+6+6+6+6=

L E A R N A ND C ONNEC T We can use equal groups, arrays, and multiplication sentences to show multiplication.

Equal Groups

Array

4 types of chocolate with 5 of each type

5 Columns

Multiplication Sentence Four times five equals twenty.

4 Rows

4 × 5 = 20 There are 20 chocolates.

AP P LY Fill in the correct numbers. 1.

4 + 4 + 4 + 4 + 4 = 20 5 times 4 = 20 5 × 4 = 20

+ + + + times = 27 × = 27

+ + = 12 times = 12 × = 12

Vocabulary Array - a grid with rows and columns that shows a multiplication fact

100

Level D

| Chapter 5 - 1

| Lighthouse MATH

= 27

+ + + + times = 25 × = 25

= 25

Exercise | 5 - 1 Name

Shade in boxes to make an array. Count to find the total.

3×4

= 12

7×1

4×6

2×6

Draw an array. Solve. 5. Jay is baking cookies. His cookie sheet has 5 rows of cookies with 4 cookies in each row. How many cookies are on the cookie sheet?

6. Tim is planting a garden. He plants 3 rows of bell peppers and puts 6 plants in each row. How many pepper plants does he plant? 7. A chocolate bar has 8 squares in each row. There are 4 rows. How many squares are there?

CH AL L ENGE 8. There are 24 desks in the classroom. Draw 3 different arrays to show how the desks could be arranged.

Level D

| Chapter 5 - 1

| Lighthouse MATH

101

5 - 2 | Multiplication Facts 2 and 3 Fill in the blanks. DAILY REV IE W

, 6, 8,

, 14,

3, 6,

, 21,

facts, you can try these tricks.

To multiply a number by 3, you can add it three times.

2×4 Double 4 is 8.

3×3 3+3+3=9

AP P LY

Complete the times tables.

2 Times Table

2×1 = 2×2 = 2×3 = 2×4 = 2×5 = 2×6 = 2×7 = 2×8 = 2×9 = 2 × 10 =

3 Times Table 3×1 = 3×2 = 3×3 = 3×4 = 3×5 = 3×6 = 3×7 = 3×8 = 3×9 = 3 × 10 =

Write the number of carrots in the garden. 3.

3+3+3= 3×3=

2+2+2+2+2= 2×5=

Draw a picture or an array to solve. 5.

102

7×3=

If you forget one of the

L E A R N A ND C ONNEC T To multiply a number by 2, you can double it.

, 12,

4×3=

Level D

| Chapter 5 - 2

2×6=

| Lighthouse MATH

2×9=

Exercise | 5 - 2 Name

Multiply. 1.

2×9=

2×7=

3×7=

2 × 10 =

9×2=

2×4=

3×9=

6×2=

10. 7 × 3 =

14. 6 × 3 =

15. 7 × 2 =

11. 1 × 2 =

13. 3 × 5 =

2 4

17.

2 × 9

18.

10 × 2

19.

2 × 10

20.

2 × 3

21.

3 × 6

22.

3 × 5

23.

9 × 3

24.

3 × 8

25.

6 × 2

26.

2 × 7

27.

3 × 7

28.

3 × 3

29.

7 × 2

30.

3 × 1

31.

4 × 3

32.

2 × 8

33.

10 × 3

16.

12. 2 × 3 =

2×5=

Read the problem. Then solve. 34. There are 9 ducks at the park. If each duck has 2 legs, how many duck legs are there in total?

35. Each tricycle has 3 wheels. How many wheels do 7 tricycles have?

CH AL L ENGE 36. If 3 × 7 is 21, what is 6 × 7?

Level D

| Chapter 5 - 2

| Lighthouse MATH

103

5 - 3 | Multiplication Facts 4 and 5 Multiply. DAILY REV IE W

2×8=

8×3=

3×4=

If you forget one of the

facts, you can try these tricks.

L E A R N A ND C ONNEC T To multiply a number by 4, you can double it, then double it again.

3×2=

To multiply a number by 5, you can skip count by fives that number of times.

4×6 Double 6 is 12. Double 12 is 24.

5×5 5, 10, 15, 20, 25

AP P LY

Complete the times tables.

4 Times Table

4×1 = 4×2 = 4×3 = 4×4 = 4×5 = 4×6 = 4×7 = 4×8 = 4×9 = 4 × 10 =

5 Times Table 5×1 = 5×2 = 5×3 = 5×4 = 5×5 = 5×6 = 5×7 = 5×8 = 5×9 = 5 × 10 =

Write the number of donuts. 3.

5+5+5+5+5+5= 6×5= 5×6=

4+4+4+4= 4×4=

Draw a picture or an array to solve. 5.

104

7×4=

4×3=

Level D

| Chapter 5 - 3

1×5=

| Lighthouse MATH

5 × 10 =

Exercise | 5 - 3 Name

Multiply. 1.

3×4=

4×2=

4×3=

4×9=

10 × 5 =

4×8=

5×8=

8×4=

10. 5 × 6 =

14. 1 × 5 =

15. 10 × 4 =

11. 5 × 1 =

12. 6 × 5 =

13. 5 × 2 =

5×9=

4 × 3

17.

4 × 1

18.

7 × 5

19.

5 × 8

20.

4 × 6

21.

3 × 5

22.

10 × 2

23.

2 × 6

24.

10 × 5

25.

5 × 4

26.

5 × 6

27.

4 × 7

28.

5 × 5

29.

10 × 3

30.

1 × 5

31.

1 × 3

32.

9 × 5

33.

5 × 7

34.

4 × 4

35.

4 × 8

36.

9 × 4 © Lighthouse Curriculum. Copying strictly prohibited.

16.

Read the problem. Then solve. 37. There are 5 rows of chairs in a classroom, and each row has 8 chairs. How many chairs are there altogether?

38. There are 6 flowers. Each flower has 5 petals. How many petals are there in all?

CH AL L ENGE 39. Which is more: 4 × 6 or 3 × 8?

Level D

| Chapter 5 - 3

| Lighthouse MATH

105

5 - 4 | Multiplication Facts 6 and 7 Multiply. DAILY REV IE W

4×4=

7×3=

10 × 3 =

If you forget one of the

facts, you can try these tricks.

L E A R N A ND C ONNEC T To multiply a number by 6, you can multiply by three and then double it.

5×9=

To multiply a number by 7, you can multiply by 6 and add one more group.

6×5 5 times 3 is 15. Double 15 is 30.

7×5 6 × 5 is 30. 30 plus 5 is 35.

AP P LY

Complete the times tables.

6 Times Table

6×1 = 6×2 = 6×3 = 6×4 = 6×5 = 6×6 = 6×7 = 6×8 = 6×9 = 6 × 10 =

7 Times Table 7×1 = 7×2 = 7×3 = 7×4 = 7×5 = 7×6 = 7×7 = 7×8 = 7×9 = 7 × 10 =

Write the number of stars. 3.

6+6+6= 3×6= 6×3=

7+7+7+7+7= 5×7= 7×5=

Draw a picture or an array to solve. 5.

106

7×4=

4×6=

Level D

| Chapter 5 - 4

1×6=

| Lighthouse MATH

7 × 10 =

Exercise | 5 - 4 Name

Multiply. 1.

1×7=

9×7=

6×7=

5×7=

6×3=

10 × 6 =

6×5=

6×6=

10. 8 × 6 =

14. 2 × 6 =

15. 3 × 7 =

12. 1 × 6 =

13. 7 × 9 =

16.

6 × 3

17.

9 × 6

18.

6 × 7

19.

3 × 4

20.

6 × 4

21.

2 × 6

22.

8 × 4

23.

7 × 8

24.

1 × 6

25.

7 × 3

26.

7 × 7

27.

6 × 8

28.

10 × 5

29.

10 × 4

30.

6 × 6

31.

4 × 3

32.

10 × 7

33.

2 × 9

34.

9 × 4

35.

7 × 2

36.

7 × 4

Read the problem. Then solve. 37. There are 6 tables, and 7 guests are seated at each table. How many guests are there?

38. A florist puts 7 tulips into every vase. If she fills 4 vases, how many tulips does she use in total?

CH AL L ENGE 39. Which is more: 3 × 6 or 2 × 7?

Level D

| Chapter 5 - 4

| Lighthouse MATH

107

11. 4 × 6 =

7×6=

5 - 5 | Multiplication Facts 8 and 9 Multiply. DAILY REV IE W

6×7=

6×3=

7×4=

If you forget one of the

facts, you can try these tricks.

L E A R N A ND C ONNEC T To multiply a number by 8, you can multiply by four and then double it.

7×3=

To multiply a number by 9, you can use your hands.

8×6 6 times 4 is 24. Double 24 is 48.

2 1

9 10

9 × 4 = 36

AP P LY

Complete the times tables.

8 Times Table

8×1 = 8×2 = 8×3 = 8×4 = 8×5 = 8×6 = 8×7 = 8×8 = 8×9 = 8 × 10 =

9 Times Table 9×1 = 9×2 = 9×3 = 9×4 = 9×5 = 9×6 = 9×7 = 9×8 = 9×9 = 9 × 10 =

Write the number of ladybugs. 3.

9+9+9+9= 4×9= 9×4=

8+8+8+8+8= 5×8= 8×5=

Draw a picture or an array to solve. 5.

108

8×4=

8×6=

Level D

| Chapter 5 - 5

2×9=

| Lighthouse MATH

7×9=

Exercise | 5 - 5 Name

Multiply. 1.

5×8=

9×6=

7×9=

8×9=

9×2=

4×9=

9×5=

10 × 8 =

10. 8 × 9 =

14. 9 × 3 =

15. 9 × 9 =

11. 8 × 7 =

12. 8 × 8 =

13. 8 × 3 =

4×8=

8 × 1

17.

6 × 8

18.

9 × 8

19.

7 × 3

20.

8 × 8

21.

9 × 3

22.

8 × 7

23.

10 × 9

24.

5 × 4

25.

9 × 9

26.

6 × 9

27.

9 × 7

28.

8 × 6

29.

9 × 4

30.

10 × 7

31.

2 × 9

32.

10 × 4

33.

4 × 8

34.

8 × 5

35.

8 × 3

36.

2 × 8 © Lighthouse Curriculum. Copying strictly prohibited.

16.

Read the problem. Then solve. 37. A classroom has 8 rows of desks. Each row has 4 desks. How many desks are in the classroom?

38. A pack of pens has 9 pens. If a teacher buys 8 packs for her class, how many pens does she have?

CH AL L ENGE 39. Which is more: 7 × 6 or 5 × 9?

Level D

| Chapter 5 - 5

| Lighthouse MATH

109

5 - 6 | Multiplication Facts 0, 1, and 10 Multiply. DAILY REV IE W

7×8=

8×8=

9×4=

9×2=

If you forget one of the

facts, you can try these tricks.

L E A R N A ND C ONNEC T A number multiplied by 0 is 0.

A number multiplied by 1 is that number.

To multiply by 10, write the number and add one zero at the end.

0 × 8 is 0.

8 × 1 is 8.

8 × 10 is 80.

AP P LY Complete the times tables.

0 Times Table

1 Times Table

0×1 = 0×2 = 0×3 = 0×4 = 0×5 = 0×6 = 0×7 = 0×8 = 0×9 = 0 × 10 =

1×1 = 1×2 = 1×3 = 1×4 = 1×5 = 1×6 = 1×7 = 1×8 = 1×9 = 1 × 10 =

10 Times Table 10 × 1 = 10 × 2 = 10 × 3 = 10 × 4 = 10 × 5 = 10 × 6 = 10 × 7 = 10 × 8 = 10 × 9 = 10 × 10 =

Write the number of oranges. 4.

10 + 10 + 10 = 3 × 10 = 10 × 3 =

1+1+1+1= 4×1= 1×4=

Draw a picture or an array to solve. 6.

110

7×1=

4×0=

Level D

| Chapter 5 - 6

1×6=

| Lighthouse MATH

5 × 10 =

Exercise | 5 - 6 Name

Multiply. 1.

9 × 10 =

6×1=

1×3=

10 × 5 =

10 × 3 =

8×1=

10 × 10 =

10 × 9 =

10. 10 × 6 =

14. 7 × 0 =

15. 9 × 1 =

11. 1 × 5 =

12. 8 × 0 =

13. 1 × 0 =

0×3=

10 × 3

17.

4 × 4

18.

10 × 6

19.

10 × 2

20.

7 × 8

21.

4 × 1

22.

1 × 3

23.

7 × 1

24.

9 × 0

25.

10 × 8

26.

8 × 3

27.

6 × 1

28.

7 × 7

29.

10 × 3

30.

8 × 0

31.

3 × 3

32.

3 × 0

33.

10 × 4 © Lighthouse Curriculum. Copying strictly prohibited.

16.

Read the problem. Then solve. 34. Each jump rope is 10 feet long. If you lay 6 jump ropes end-to-end, what is the total length?

35. Each branch has 1 bud. There are 7 branches. How many buds are there?

CH AL L ENGE 36. Which would you rather have: $1,000 × 0 or $36.00 × 1? Why?

Level D

| Chapter 5 - 6

| Lighthouse MATH

111

5 - 7 | Multiplication Facts 11 and 12 Multiply. DAILY REV IE W

8×7=

3×7=

0×6=

If you forget one of the

facts, you can try these tricks.

L E A R N A ND C ONNEC T A single-digit number multiplied by 11 is that digit repeated.

Double-digit numbers multiplied by 11 can be figured out this way.

To multiply a number by 12, you can multiply by 10 and then add double that number.

11 × 12

11 × 6 = 66

2×4=

Write 1 ___ 2

Add 1 + 2 = 3

3 × 12 3 × 10 = 30; double 3 is 6. 30 + 6 = 36

Put 3 in the middle → 132

AP P LY

Complete the times tables.

11 Times Table

12 Times Table

11 × 1 = 11 × 2 = 11 × 3 = 11 × 4 = 11 × 5 = 11 × 6 = 11 × 7 = 11 × 8 = 11 × 9 = 11 × 10 = 11 × 11 = 11 × 12 =

12 × 1 = 12 × 2 = 12 × 3 = 12 × 4 = 12 × 5 = 12 × 6 = 12 × 7 = 12 × 8 = 12 × 9 = 12 × 10 = 12 × 11 = 12 × 12 =

Write the number of smiley faces. 3.

11 + 11 + 11 + 11 = 4 × 11 = 11 × 4 =

12 + 12 + 12 = 3 × 12 = 12 × 3 =

Draw a picture or an array to solve. 5.

112

7 × 11 =

Level D

12 × 4 =

| Chapter 5 - 7

| Lighthouse MATH

11 × 5 =

Exercise | 5 - 7 Name

Multiply. 1.

4 × 12 =

5 × 11 =

8 × 11 =

12 × 11 =

2 × 11 =

6 × 11 =

12 × 12 =

9 × 11 =

10. 12 × 6 =

14. 0 × 12 =

15. 11 × 7 =

11. 6 × 12 =

12. 11 × 11 =

13. 12 × 2 =

12 × 9 =

12 × 10

17.

6 × 9

18.

8 × 4

19.

8 × 9

20.

11 × 3

21.

8 × 6

22.

10 × 6

23.

12 × 8

24.

6 × 5

25.

9 × 5

26.

12 × 1

27.

11 × 4

28.

12 × 3

29.

10 × 11

30.

4 × 4

31.

5 × 4

32.

5 × 8

33.

12 × 5 © Lighthouse Curriculum. Copying strictly prohibited.

16.

Read the problem. Then solve. 34. A student reads 11 pages of a book every night. If she reads for 5 nights, how many pages will she read?

35. A dozen eggs is equal to 12 eggs. If a baker buys 8 dozen eggs, how many eggs does he have?

CH AL L ENGE 36. Explain how you could use a tens fact to solve 4 × 11 and 5 × 12.

Level D

| Chapter 5 - 7

| Lighthouse MATH

113

5 - 8 | Chapter Review Multiply. DAILY REV IE W

6×8=

8×5=

9×4=

3×9=

L E T ' S REV I EW Complete the times tables. 1.

2 Times Table

2×1 = 2×2 = 2×3 = 2×4 = 2×5 = 2×6 = 2×7 = 2×8 = 2×9 = 2 × 10 =

5 Times Table

8 Times Table

6 Times Table

9 Times Table 9×1 = 9×2 = 9×3 = 9×4 = 9×5 = 9×6 = 9×7 = 9×8 = 9×9 = 9 × 10 =

Level D

| Chapter 5 - 8

| Lighthouse MATH

4 Times Table 4×1 = 4×2 = 4×3 = 4×4 = 4×5 = 4×6 = 4×7 = 4×8 = 4×9 = 4 × 10 =

6×1 = 6×2 = 6×3 = 6×4 = 6×5 = 6×6 = 6×7 = 6×8 = 6×9 = 6 × 10 =

8×1 = 8×2 = 8×3 = 8×4 = 8×5 = 8×6 = 8×7 = 8×8 = 8×9 = 8 × 10 =

114

3×1 = 3×2 = 3×3 = 3×4 = 3×5 = 3×6 = 3×7 = 3×8 = 3×9 = 3 × 10 =

5×1 = 5×2 = 5×3 = 5×4 = 5×5 = 5×6 = 5×7 = 5×8 = 5×9 = 5 × 10 = 7.

3 Times Table

7 Times Table 7×1 = 7×2 = 7×3 = 7×4 = 7×5 = 7×6 = 7×7 = 7×8 = 7×9 = 7 × 10 =

10 Times Table 10 × 1 = 10 × 2 = 10 × 3 = 10 × 4 = 10 × 5 = 10 × 6 = 10 × 7 = 10 × 8 = 10 × 9 = 10 × 10 =

Exercise | 5 - 8 Name

Multiply. 1.

5 × 10 =

1×8=

6×4=

4 × 12 =

9×6=

9×4=

6×7=

8×8=

10. 6 × 11 =

14. 2 × 4 =

15. 8 × 9 =

11. 5 × 2 =

12. 8 × 5 =

13. 3 × 4 =

5×5=

16.

7 × 8

17.

6 × 6

18.

3 × 8

19.

9 × 5

20.

2 × 8

21.

9 × 9

22.

7 × 7

23.

7 × 2

24.

8 × 6

25.

9 × 8

26.

7 × 5

27.

3 × 0

28. A tricycle has 3 wheels. How many wheels do 4 tricycles have?

29. A ticket to the zoo costs $6. How much does it cost to buy 5 tickets?

CH AL L ENGE 30. Multiply to find the cost.

Order Form

SALE Hammers

Screwdrivers

Bolts

Wrenches

Level D

| Chapter 5 - 8

Number of tools

Equation

Total Cost

5 4 9 Total Cost

| Lighthouse MATH

115

Read the problem. Then solve.

5 - 9 | Cumulative Review

Solve. 1.

17 − 9

8 × 5

2 × 8

5 + 3

9 + 3

1 × 1

18 − 9

11 − 4

11 − 8

10.

2 + 2

11.

7 + 5

12.

1 × 3

13.

17 − 8

14.

1 + 4

15.

3 + 5

16.

5 × 6

17.

3 × 9

18.

8 + 8

19.

1 + 1

20.

8 × 4

21.

8 + 1

22.

6 + 4

23.

11 − 2

24.

8 × 9

25.

5 × 3

26.

8 − 3

27.

8 − 5

28.

12 − 3

29.

2 × 4

30.

6 + 1

31.

3 − 1

32.

9 − 6

33.

7 × 7

34.

9 + 6

35.

7 × 5

36.

9 + 1

37.

8 − 1

38.

15 − 9

39.

15 − 8

40.

8 + 4

41.

6 − 5

42.

3 × 2

43.

4 − 3

44.

7 − 5

45.

4 × 8

46.

5 + 2

47.

6 + 3

48.

15 − 7

49.

2 × 9

50.

6 × 8

51.

4 × 4

52.

7 + 7

53.

8 × 6

54.

5 × 4

55.

8 + 3

56.

5 + 6

57.

4 + 15

58.

9 − 2

59.

4 × 6

60.

16 − 8

61.

6 + 2

62.

12 − 9

63.

3 × 8

116

Level D

| Chapter 5 - 9

| Lighthouse MATH

Exercise | 5 - 9 Name

Add. 1.

266 + 560

248 + 690

347 + 583

9,081 + 7,594

2,750 + 2,571

9,676 + 1,232

3,222 9,973 + 8,541

8,549 4,836 + 4,950

2,719 7,110 + 2,999

10.

5,610 6,304 + 3,264

11.

2,240 5,595 + 4,939

12.

2,469 1,823 + 5,418

Subtract. 13.

628 − 355

14.

486 − 288

15.

816 − 159

16.

5,878 − 2,884

17.

9,906 − 5,734

18.

4,997 − 3,608

19.

314 − 64

20.

729 − 247

21.

3,284 − 717

22.

5,412 − 654

23.

1,856 − 72

24.

3,428 − 98

25.

4 × 4

26.

6 × 6

27.

7 × 7

28.

8 × 2

29.

8 × 4

30.

5 × 4

31.

9 × 9

32.

2 × 2

33.

5 × 5

34.

2 × 5

35.

5 × 3

36.

3 × 3

Write the number. 37. six million, four hundred seventy-four thousand, one hundred thirty-two 38. sixty-nine thousand, one hundred ninety-four 39. two hundred fifty-two thousand, five hundred sixty-nine 40. four hundred fifty thousand, six hundred three

Level D

| Chapter 5 - 9

| Lighthouse MATH

117

Multiply.

6 C H A P T E R

118

In Chapter 6 we will learn about

Multiplying a Two- or Three-Digit Number In this chapter, we will be multiplying two- and three-digit numbers. When multiplying large numbers, it is important to keep your work organized. • We will learn tips for multiplying multiples of 10, 100, and 1,000. • We will multiply numbers by lining up their place values and working through one place value at a time. • We will learn how to regroup when the product is larger than 9. • We will learn how to multiply money amounts by a whole number.

119

6 - 1 | Multiplying by Multiples of 10, 100, and 1,000 Multiply. DAILY REV IE W

8×8=

3×3=

6×4=

3×4=

L E A R N A ND C ONNEC T To multiply by a multiple of ten, first multiply the numbers without the zeros. Then, add the zeros to the end of the answer. Multiply the numbers without the zeros.

Add the zeros to the end of the answer.

3×5= 15 3 × 50 = 15 3 × 500 = 15 3 × 5,000 = 15

3×5= 15 3 × 50 = 150 3 × 500 = 1,500 3 × 5,000 = 15,000

AP P LY

Use patterns to multiply. 1. 3 × 1 =

2. 8 × 1 =

3. 10 × 1 =

3 × 10 =

8 × 10 =

10 × 10 =

3 × 100 =

8 × 100 =

10 × 100 =

3 × 1,000 =

8 × 1,000 =

10 × 1,000 =

4. 5 × 9 =

5. 2 × 3 =

6. 4 × 6 =

5 × 90 =

2 × 30 =

4 × 60 =

5 × 900 =

2 × 300 =

4 × 600 =

5 × 9,000 =

2 × 3,000 =

4 × 6,000 =

120

Level D

| Chapter 6 - 1

| Lighthouse MATH

Exercise | 6 - 1 Name

Multiply. 40 × 5

700 × 2

1,000 × 3

90 × 4

200 × 8

4,000 × 6

6,000 × 7

80 × 6

300 × 9

10.

10 × 8

11.

700 × 4

12.

500 × 2

13.

100 × 9

14.

2,000 × 4

15.

50 × 7

16.

8,000 × 5

17.

60 × 3

18.

900 × 5

19.

600 × 8

20.

50 × 6

21.

200 × 3

22.

3,000 × 2

23.

40 × 8

24.

300 × 7

25.

9,000 × 12

26.

60 × 9

27.

800 × 5

28.

1,000 × 4

29.

20 × 7

30.

100 × 2 © Lighthouse Curriculum. Copying strictly prohibited.

Read the problem. Then solve. 31. Each city bus is 40 feet long. If 6 city buses are lined up end-to-end, what is the total length?

32. A company makes $3,000 a month. How much does it make after 7 months?

CH AL L ENGE 33. What is 5 × 900,000?

Level D

| Chapter 6 - 1

| Lighthouse MATH

121

6 - 2 | Multiplying Two Multiples of 10, 100, and 1,000 Multiply. DAILY REV IE W

2 × 100 =

5 × 30 =

6 × 800 =

3,000 × 7 =

L E A R N A ND C ONNEC T To multiply two multiples of ten, multiply the numbers without the zeros. Then, count up the zeros and add them to the end of the answer. Multiply the numbers without the zeros.

Add all the zeros to the end of the answer.

50 × 7 = 35 50 × 70 = 35 50 × 700 = 35 50 × 7,000 = 35

50 × 7 = 350 50 × 70 = 3,500 50 × 700 = 35,000 50 × 7,000 = 350,000

AP P LY

Use patterns to multiply. 1. 80 × 4 =

2. 30 × 6 =

3. 70 × 7 =

80 × 40 =

30 × 60 =

70 × 70 =

80 × 400 =

30 × 600 =

70 × 700 =

80 × 4,000 =

30 × 6,000 =

70 × 7,000 =

4. 300 × 9 =

5. 600 × 5 =

6. 200 × 8 =

300 × 90 =

600 × 50 =

200 × 80 =

300 × 900 =

600 × 500 =

200 × 800 =

300 × 9,000 =

600 × 5,000 =

200 × 8,000 =

122

Level D

| Chapter 6 - 2

| Lighthouse MATH

Exercise | 6 - 2 Name

40 × 50

700 × 20

5,000 × 30

90 × 40

200 × 80

600 × 70

8,000 × 600

30 × 90

1,000 × 40

10.

2,000 × 70

11.

80 × 20

12.

7,000 × 60

13.

500 × 80

14.

900 × 10

15.

900 × 50

16.

300 × 70

17.

4,000 × 50

18.

400 × 60

19.

2,000 × 30

20.

800 × 90

21.

6,000 × 2,000

22.

500 × 60

23.

800 × 900

24.

700 × 40

25.

6,000 × 30

26.

400 × 70

27.

3,000 × 90

28.

500 × 20

29.

600 × 80

30.

700 × 50 © Lighthouse Curriculum. Copying strictly prohibited.

Multiply.

Read the problem. Then solve. 31. A train car can carry 5,000 pounds. If there are 50 train cars, what is the total weight the train can carry?

32. There are 60 minutes in an hour. How many minutes are in 30 hours?

CH AL L ENGE 33. What is 800,000 × 700,000?

Level D

| Chapter 6 - 2

| Lighthouse MATH

123

6 - 3 | Multiplying Two-Digit by One-Digit Numbers (No Regrouping) Solve. DAILY REV IE W

40 � 50 =

70 � 20 =

600 � 40 =

L E A R N A ND C ONNEC T A teacher hands out 3 notebooks to each student. There are 21 students in the class. How many notebooks are there in all? To find the number of notebooks, multiply by . Set up the problem.

Multiply the tens.

Multiply the ones.

Put the bigger number on top. 21 × 3

21 × 3 63

21 × 3 3

There are 63 notebooks in all.

AP P LY Use the pictures to help you solve the multiplication problems. 1.

2. 14 × 2

124

31 × 3

Level D

| Chapter 6 - 3

| Lighthouse MATH

Exercise | 6 - 3 Name

Multiply. 1.

41 � 3

23 � 2

13 � 2

38 � 1

33 � 3

22 � 3

41 � 2

75 � 1

11 10. × 5

33 × 2

11. 21 � 2

17 12. � 1

11 13. � 9

12 14. � 3

11 15. � 6

21 16. � 3

34 17. � 2

11 18. � 7

12 19. � 3

12 20. � 4

21. 13 × 2

22. 10 × 3

23. 36 × 1

24. 14 × 2

25. 13 × 3

26. 12 × 2

27. 22 × 2

28. 16 × 1

29. 23 × 3

30. 99 × 0

Read the problem. Then solve. 32. There are 24 hours in a day. How many hours are there in 2 days?

31. An art teacher has 3 boxes of paint. Each box contains 32 tubes of paint. What is the total number of paint tubes?

CH AL L ENGE 33. What is 35 � 3? Show how you found the answer.

Level D

| Chapter 6 - 3

| Lighthouse MATH

125

Rewrite and multiply.

6 - 4 | Regrouping in Multiplication Multiply. 1.

DAILY REV IE W

14 � 2

32 � 3

42 � 2

11 � 8

L E A R N A ND C ONNEC T When multiplying, if an answer in any place is more than 9, we need to regroup. Break the answer into tens and ones and carry the tens. To multiply the next place value, first multiply the numbers from the problem. Then, add the number that was carried. Set up the problem. 23 × 4

Multiply the ones. Regroup. 4 × 3 = 12

Multiply the tens. Add the extra.

Carry the 1.

4×2=8

23 × 4 92

23 × 4 2

23 × 4

8+1=9

AP P LY Use the pictures to help solve the multiplication problem. 1.

2. 69 × 2

126

Level D

35 × 3

| Chapter 6 - 4

| Lighthouse MATH

Exercise | 6 - 4 Name

Multiply. 1.

43 × 7

58 × 3

19 × 2

84 × 7

14 × 6

34 × 3

93 × 9

75 × 7

98 10. × 9

54 × 5

11. 12 × 2

46 12. × 6

50 13. × 5

98 14. × 3

14 15. × 8

38 16. × 6

15 17. × 4

65 18. × 4

73 19. × 8

18 20. × 5

21. 52 × 6

22. 59 × 3

23. 47 × 2

24. 32 × 3

25. 97 × 6

26. 81 × 9

27. 51 × 7

28. 21 × 7

29. 59 × 7

30. 16 × 4

Rewrite and multiply.

Read the problem. Then solve. 31. A candy company packs 7 pieces of candy into each bag. If they fill 43 bags, what is the total number of candies?

32. A large garden has 55 rows of rose bushes. Each row has 9 bushes. How many rose bushes are there in the garden?

CH AL L ENGE 33. What is 627 � 3?

Level D

| Chapter 6 - 4

| Lighthouse MATH

127

6 - 5 | Multiplying Two-Digit by One-Digit Numbers (With Regrouping) Multiply. 1.

DAILY REV IE W

52 � 4

25 � 3

36 � 7

26 � 3

L E A R N A ND C ONNEC T There are 4 rows of plants in David's garden. Each row has 45 plants. How many plants are there in all? To find the number of plants, multiply

Multiply the ones. Regroup. 4 × 5 = 20

. Multiply the tens. Add the extra.

Carry the 2.

4 × 4 = 16

16 + 2 = 18 2

45 × 4 180

45 × 4 0

There are 180 plants.

AP P LY Fill in the missing numbers. 1.

4 5 6 × 7

4. 2 3 × 4

8 2 × 9

7. 8 4 × 3

128

5 1 × 2

4 4 × 3

8. 7 4 × 8

Level D

9. 9 1 × 5

| Chapter 6 - 5

| Lighthouse MATH

10. 3 3 × 2

5 2 × 8

Exercise | 6 - 5 Name

Multiply. 1.

45 × 5

52 × 3

14 × 4

28 × 2

92 × 5

86 × 2

72 × 8

92 × 8

63 10. × 6

43 × 7

11. 82 × 5

19 12. × 3

55 13. × 4

18 14. × 6

64 15. × 7

90 16. × 4

45 17. × 3

29 18. × 7

81 19. × 9

17 20. × 6

21. 15 × 6

22. 17 × 9

23. 46 × 2

24. 83 × 4

25. 44 × 3

26. 4 × 72

27. 38 × 2

28. 26 × 3

29. 51 × 7

30. 42 × 5

Rewrite and multiply.

Read the problem. Then solve. 32. Each student in class has 8 pens in their desk. If there are 32 students in class, how many pens are in all the desks?

31. A candy bar costs 97¢. How much will Thomas spend if he buys 8 candy bars?

CH AL L ENGE 33. What is 865 � 7?

Level D

| Chapter 6 - 5

| Lighthouse MATH

129

6 - 6 | Multiplying Three-Digit by One-Digit Numbers Solve. 1.

DAILY REV IE W

72 � 5

64 � 4

52 � 9

48 � 4

L E A R N A ND C ONNEC T Raymond unpacks 4 boxes of soup cans. Each box holds 125 cans of soup. How many soup cans does he unpack altogether? To find the total number of soup cans, multiply by . Multiply the ones. Regroup.

Multiply the tens. Add the extra. Regroup.

Multiply the hundreds. Add the extra.

4 × 5 = 20 Carry the 2.

4 × 2 = 8 8 + 2 = 10 Carry the 1.

4×1=4 4+1=5

125 × 4 0

125 × 4 00

125 × 4 500

Raymond unpacks 500 soup cans.

AP P LY Use the pictures to help you solve the multiplication. 1.

2. 136 × 2

130

Level D

232 × 3

| Chapter 6 - 6

| Lighthouse MATH

Exercise | 6 - 6 Name

Multiply. 1.

221 × 4

562 × 3

116 × 4

328 × 2

492 × 5

108 × 2

702 × 8

960 × 8

10. 713 × 6

143 × 7

11. 682 × 5

12. 219 × 3

13. 515 × 4

14. 186 × 6

15. 641 × 7

16. 920 × 4

17. 145 × 3

18. 239 × 7

19. 421 × 9

20. 217 × 6

21. 315 × 3

22. 127 × 4

23. 426 × 5

24. 833 × 4

25. 114 × 7

26. 538 × 2

27. 225 × 7

28. 151 × 6

Rewrite and multiply.

Read the problem. Then solve. 29. David bikes 216 miles a week going to and from work. At this rate, how many miles will he bike after 4 weeks?

30. There are 304 pumpkin seeds in a snack bag. How many pumpkin seeds are there in 9 snack bags?

CH AL L ENGE 31. What is 9,523 � 3?

Level D

| Chapter 6 - 6

| Lighthouse MATH

131

6 - 7 | More Multiplying Three-Digit by One-Digit Numbers Multiply. 1.

DAILY REV IE W

26 × 9

39 × 9

125 × 3

354 × 2

L E A R N A ND C ONNEC T Joseph spends 147 minutes on homework each week. How many minutes does he spend on homework in 4 weeks? To find the number of minutes he spends on homework, multiply by . Multiply the ones.

Multiply the tens. Add the extra. Regroup.

Multiply the hundreds. Add the extra.

4 × 7 = 28 Carry the 2.

4 × 4 = 16 16 + 2 = 18 Carry the 1.

4×1=4 4+1=5

147 × 4 88

147 × 4 8

147 × 4 588

Joseph spends 588 minutes on homework.

AP P LY Fill in the missing numbers. 1.

2. 8 3 1 × 5

3 3 2 × 4

7. 7 1 4 × 3

132

4. 2 5 3 × 4

8. 3 0 4 × 5

Level D

5. 9 4 1 × 8

9. 4 2 1 × 2

| Chapter 6 - 7

4 8 4 × 3

10. 3 3 3 × 7

| Lighthouse MATH

5 7 1 × 3

Exercise | 6 - 7 Name

Multiply. 1.

478 × 2

120 × 6

181 × 5

529 × 4

637 × 6

789 × 4

945 × 4

430 × 6

10. 437 × 7

595 × 3

11. 642 × 6

12. 144 × 7

13. 443 × 3

14. 896 × 8

15. 434 × 1

16. 165 × 2

17. 834 × 5

18. 307 × 4

19. 245 × 9

20. 862 × 8

21. 775 × 5

22. 856 × 7

23. 940 × 3

24. 390 × 3

25. 753 × 4

26. 618 × 6

27. 626 × 9

28. 767 × 5

Read the problem. Then solve. 29. A store orders 5 crates of water bottles. Each crate has 288 bottles. How many bottles does the store order in all?

30. 904 people visit the zoo each day. How many people have visited the zoo after 4 days?

CH AL L ENGE 31. What is 8,542 � 4?

Level D

| Chapter 6 - 7

| Lighthouse MATH

133

Rewrite and multiply.

6 - 8 | Multiplying Money Multiply. 1.

DAILY REV IE W

161 × 5

608 × 4

342 × 8

922 × 6

L E A R N A ND C ONNEC T David is selling 4 pumpkins for $13.75 each. How much money will he make if he sells all of his pumpkins? To find how much money he will make, multiply by . To multiply money, ignore the dollar sign and decimal as you multiply. Then, add them to your answer at the end. Start multiplying from the right. Regroup if needed. Move left to the next place value and repeat. 2

$13.75 × 4 0

3 2

13 2

$13.75 × 4 00

Place the $ and the decimal point.

132

$13.75 × 4 500

$13.75 × 4 55.00

132

$13.75 × 4 $55.00

David will make $55.00 if he sells all his pumpkins.

AP P LY Fill in the missing numbers. 1.

2. $ 7 . 2 7 7

× $

134

3. $ 3 . 8 2 3

× $

Level D

| Chapter 6 - 8

4. $ 9 . 6 3 6

× $

| Lighthouse MATH

$ 4 . 5 5 8

× $

Exercise | 6 - 8 Name

Multiply to solve. Remember to add a dollar sign and decimal point. 1.

$5.46 × 9

$3.68 × 8

$2.41 × 3

$9.02 × 7

$12.55 × 4

$8.39 × 2

$4.59 × 5

$23.75 × 2

$8.03 × 4

$7.45 10. × 6

$6.28 11. × 4

12. $32.40 × 3

13. $8.32 × 5

14. $6.88 × 4

15. $4.52 × 3

16. $9.45 × 6

17. $14.65 × 2

18. $65.73 × 5

Rewrite and multiply.

Read the problem. Then solve. 20. Josh washes cars after school. He charges $11.50 per car. If he washed 9 cars, how much money did he make?

19. Max visits a local museum 3 times a week. If tickets cost $5.25 each, how much will Max spend each week?

CH AL L ENGE Find the missing digits.

21.

Level D

$7.15 × $64.35

| Chapter 6 - 8

22.

$45.___0 × 3 $1___6.20

| Lighthouse MATH

135

6 - 9 | Chapter Review Multiply. 1.

DAILY REV IE W

$3.36 × 2

$4.03 × 6

$6.59 × 5

$8.59 × 8

L E T ' S REV I EW Multiplying by Multiples of 10

Multiplying by By a One-Digit Number

Multiply the numbers without zeros. Add all the zeros to the end of the answer.

Start multiplying from the right. Regroup if needed. Move left to the next place value and repeat.

50 × 700 = 3,500

632 × 4 2,528 Multiplying Money Multiply from right to left. Place the decimal point and the dollar sign. 12 1

$12.43 × 5 $62.15

AP P LY Solve. 1.

78 × 6

80 × 8

34 × 9

63 × 3

40 × 5

17 × 2

57 × 9

42 × 8

136

Level D

| Chapter 6 - 9

| Lighthouse MATH

Exercise | 6 - 9 Name

Multiply to solve. Remember to add a dollar sign and decimal point when necessary. 1.

277 × 8

689 × 3

843 × 3

256 × 3

$1.54 × 6

$5.93 × 9

$9.18 × 2

$6.13 × 7

$45.18 × 8

10. $69.96 × 6

11. $38.58 × 9

12. $16.92 × 5

13. 68 × 7

14. 70 × 2

15. 397 × 3

16. $3.75 × 8

17. $8.50 × 3

18. $10.68 × 2

Read the problem. Then solve. 19. A restaurant has 2 boxes of ketchup packets. Each box has 342 packets. How many ketchup packets are there in all?

20. A bakery makes 5 cakes each day. How many cakes will the bakery make in 212 days?

CH AL L ENGE 21. What is 3,002 � 9?

Level D

| Chapter 6 - 9

| Lighthouse MATH

137

Rewrite and multiply.

6 - 10 | Cumulative Review

Solve. 1.

9 + 8

9 + 6

14 − 6

7 + 1

5 + 5

8 + 4

5 × 9

2 × 7

3 + 7

10.

4 + 6

11.

5 × 5

12.

2 + 9

13.

8 − 2

14.

1 + 3

15.

10 − 3

16.

7 × 7

17.

9 + 4

18.

1 × 4

19.

7 + 2

20.

13 − 5

21.

6 + 9

22.

9 × 7

23.

2 + 3

24.

17 − 8

25.

1 + 5

26.

9 − 7

27.

7 − 4

28.

12 − 5

29.

4 + 8

30.

8 × 1

31.

4 × 7

32.

9 − 2

33.

9 − 4

34.

7 − 2

35.

12 − 4

36.

4 + 3

37.

1 + 8

38.

7 − 3

39.

5 × 7

40.

4 × 9

41.

10 − 4

42.

2 + 6

43.

1 + 2

44.

7 × 5

45.

15 − 6

46.

3 + 3

47.

8 × 8

48.

2 × 4

49.

7 + 7

50.

5 + 2

51.

5 × 1

52.

3 + 2

53.

7 + 8

54.

6 − 3

55.

5 + 9

56.

12 − 9

57.

14 − 7

58.

8 + 3

59.

6 × 3

60.

9 + 2

61.

17 − 9

62.

5 × 4

63.

13 − 8

138

Level D

| Chapter 6 - 10

| Lighthouse MATH

Exercise | 6 - 10 Name

Add. 1.

633 + 311

291 + 520

141 + 280

4,949 + 4,328

8,024 + 1,749

7,773 + 1,938

Subtract. 7.

504 − 376

983 − 407

287 − 217

10.

5,972 − 1,774

11.

9,072 − 2,630

12.

3,432 − 1,259

13.

3,000 − 2,247

14.

6,000 − 1,977

15.

3,000 − 1,127

16.

302 − 98

17.

6,004 − 4,507

18.

5,005 − 2,487

563 × 8

19.

19 × 9

20.

63 × 6

21.

88 × 2

22.

793 × 9

23.

239 × 5

24.

25.

40 × 5

26.

700 × 2

27.

1,000 × 3

28.

90 × 4

29.

200 × 8

30. 4,000 × 7

Round each number to the highest place value. 31. 26

32. 71

33. 45

34. 369

35. 409

36. 2,953

37. 8,199

38. 1,526

39. 24,098

40. 89,258

Level D

| Chapter 6 - 10

| Lighthouse MATH

139

Multiply.

7 C H A P T E R

140

In Chapter 7 we will learn about

Double-Digit Multiplication In this chapter, we will be multiplying by a two-digit number. When multiplying large numbers, it is important to keep your work organized. • We will learn a trick to multiply multidigit numbers by a multiple of ten. • We will learn the steps to multiply two two-digit numbers. • We will learn the steps to multiply a three-digit number by a two-digit number. • We will round to estimate products. • We will apply what we learned to real-world problems.

141

7 - 1 | Multiplying a Two-Digit or Three-Digit Number by a Multiple of Ten Multiply. 1.

DAILY REV IE W

376 × 8

473 × 5

594 × 5

189 × 3

L E A R N A ND C ONNEC T Ben is counting his steps while walking. He walks 28 steps per minute. How many steps will he walk in 60 minutes? To find the number of steps, we multiply

Set up the problem. Put the number that ends in zero on bottom.

Write a 0.

28 × 60

28 × 60 0

28 × 60 80

Multiply the ones.

Multiply the tens.

28 × 60 1,680

Ben walks 1,680 steps.

AP P LY Write a zero. Then multiply. 1.

4 2 7 0

0 6. 2 4 3 0

0 7.

142

3 1 9 0

9 6 4 0

2 9 3 × 2 0

4 4 8 0

Level D

| Chapter 7 - 1

0 10.

9. 8 1 5 0

3 6 8 3 0

1 4 3 × 2 0

| Lighthouse MATH

3 5 7 8 0

Exercise | 7 - 1 Name

Multiply. 1.

73 × 20

11 × 40

87 × 50

42 × 30

71 × 80

73 × 90

18 × 70

88 × 10

27 10. × 60

27 × 70

11. 41 × 50

81 12. × 30

82 13. × 80

52 14. × 10

83 15. × 30

16. 315 × 30

17. 953 × 50

18. 926 × 50

19. 842 × 10

20. 908 × 90

21. 90 × 90

22. 41 × 50

23. 57 × 80

24. 18 × 40

25. 60 × 40

26. 48 × 80

27. 84 × 60

28. 86 × 30

Rewrite and multiply.

Read the problem. Then solve. 29. A school serves 346 meals a day. How many meals will it serve in 20 school days?

30. A farmer has 25 boxes of apples. Each box contains 30 pounds of apples. What is the total weight of the apples?

CH AL L ENGE 31. What is 65 � 400?

Level D

| Chapter 7 - 1

| Lighthouse MATH

143

7 - 2 | Multiplying by Two-Digit Numbers Multiply. 1.

DAILY REV IE W

84 × 80

74 × 50

66 × 50

95 × 70

L E A R N A ND C ONNEC T When multiplying two-digit numbers, we first multiply the ones digit from the bottom number by the top number. Then, write a zero below the answer. Now we can multiply the tens digit in the bottom number by the top number. We add the two answers together to get the final answer.

Multiply by the ones. 32 × 23 96

32 × 23 6

Multiply by the tens.

Write a zero. 32 × 23 96 0

32 × 23 96 40

Add.

32 × 23 96 640

32 × 23 96 + 640 736

AP P LY Multiply. 1.

144

2. ×

3 1 3 2

7 2 3 4

Level D

1 2 1 4

| Chapter 7 - 2

9 1 3 2

3 3 1 3

| Lighthouse MATH

Exercise | 7 - 2 Name

Multiply. 1.

22 × 12

73 × 12

91 × 23

52 × 23

71 × 24

81 × 44

10. 21 × 44

11. 22 × 41

12. 21 × 12

15. 63 × 22

16. 92 × 13

17. 82 × 24

18. 82 × 32

13. 62 × 22

14. 32 × 22

41 × 21

93 × 33

13 × 31

Rewrite and multiply. 20. 41 × 13

21. 21 × 31

22. 83 × 22

Read the problem. Then solve. 23. A large building has 34 floors. Each floor has 21 rooms. How many rooms are in the building?

24. A camp sells T-shirts for $14 each. If they sell 12 T-shirts, how much money do they make?

CH AL L ENGE 25. What is 69 � 45?

Level D

| Chapter 7 - 2

| Lighthouse MATH

145

19. 92 × 23

7 - 3 | Multiplying by Two-Digit Numbers (With Regrouping) Multiply. 1.

DAILY REV IE W

23 × 23

93 × 33

14 × 21

13 × 13

L E A R N A ND C ONNEC T Mark buys 24 bags of nuts. Each bag weighs 83 ounces. How much do all the bags weigh? To find the total weight, multiply by .

Multiply by the ones. 1

83 × 24 332

83 × 24 2

Write a zero. Erase any numbers you carried.

Multiply by the tens.

83 × 24 332 0

83 × 24 332 60

Add.

83 × 24 332 1660

83 × 24 332 + 1660 1,992

The nuts weigh 1,992 ounces.

AP P LY Multiply. 1.

146

2. ×

8 6 7 3

7 1 3 8

Level D

2 6 4 5

| Chapter 7 - 3

3 3 2 8

8 8 3 4

| Lighthouse MATH

Exercise | 7 - 3 Name

Multiply. 1.

54 × 45

16 × 27

29 × 69

18 × 41

38 × 33

48 × 86

65 × 72

17 × 48

10. 89 × 70

14. 24 × 67

15. 41 × 42

11. 19 × 89

12. 92 × 36

13. 62 × 23

54 × 75

Rewrite and multiply. 17. 12 × 46

18. 54 × 43

19. 57 × 33

Read the problem. Then solve. 20. A bakery makes 36 loaves of bread every day. Each loaf is cut into 21 slices. How many slices of bread does the bakery make in a day?

21. A large parking lot has 41 rows. Each row can fit 12 cars. What is the total number of cars that can park in the lot?

CH AL L ENGE 22. What is 236 � 45?

Level D

| Chapter 7 - 3

| Lighthouse MATH

147

16. 86 × 92

7 - 4 | Multiplying Three-Digit by Two-Digit Numbers (With Regrouping) Multiply. 1.

DAILY REV IE W

71 × 83

97 × 68

88 × 61

78 × 46

L E A R N A ND C ONNEC T Elon reads 15 pages every day. How many pages will he have read after 365 days? To find the number of pages Elon will read, multiply by .

Multiply by the ones. 2

365 × 15 5

365 × 15 25

Add a zero. Erase any numbers you carried.

365 × 15 1825

365 × 15 1825 0

Multiply by the tens.

365 × 15 1825 50

365 × 15 1825 650

365 × 15 1825 3650

Add.

365 × 15 1825 + 3650 5,475

Elon will read 5,475 pages.

AP P LY Multiply. 1.

6 8 4 7 2

148

3 7 5 9 8

Level D

6 6 0 4 4

| Chapter 7 - 4

1 0 8 3 8

9 5 5 3 7

| Lighthouse MATH

Exercise | 7 - 4 Name

Multiply. 1.

988 × 66

139 × 77

352 × 11

969 × 47

799 × 61

928 × 55

559 × 62

878 × 99

10. 406 × 89

14. 640 × 96

15. 406 × 80

11. 452 × 67

12. 304 × 16

13. 884 × 96

328 × 99

Rewrite and multiply. 17. 986 × 23

18. 422 × 65

16. 682 × 78

Read the problem. Then solve. 19. There are 120 tables at the school dinner with 24 people sitting at each table. How many people are at the dinner?

20. A store gets 165 cases of cereal. Each case has 12 boxes. How many boxes does the store get in all?

CH AL L ENGE 21. What is 742 � 423?

Level D

| Chapter 7 - 4

| Lighthouse MATH

149

7 - 5 | Estimating Products Round each number to the highest place value. DAILY REV IE W

2. 7,392

3. 902

4. 17,299

Round the first number.

Round the second number.

Multiply.

1,760 × 24

1. 389

L E A R N A ND C ONNEC T The Blue Creek Bike Race is 24 miles long. Each mile is 1,760 yards. About how many yards is the race? We don’t need to find an exact answer. To estimate the number of yards in the race, we can round 24 and 1,760 to the highest place value and multiply.

2,000

2,000 20

1,760 × 24

2,000 × 20 40,000

The bike race is about 4,000 yards.

AP P LY Round to the highest place value and then solve. 1.

503 × 84

682 × 78

81 × 49

455 × 63

22 × 43

292 × 65

150

Level D

| Chapter 7 - 5

| Lighthouse MATH

Exercise | 7 - 5 Name

Round to the highest place value to estimate the answer. 1.

27 × 11

21 × 17

32 × 28

53 × 19

67 × 12

78 × 14

36 × 18

41 × 22

845 × 45

10. 290 × 52

11. 560 × 40

12. 885 × 88

13. 26 × 51

14. 345 × 18

15. 915 × 52

16. 186 × 98

17. 58 × 58

18. 63 × 94

19. 223 × 43

20. 47 × 21

21. There are 17 crayons in each box, and there are 29 boxes. About how many crayons are there in total?

Read the problem. Then solve. 22. The mail room at school mails 48 letters a day. There are 19 days left of school. About how many more letters will get mailed before school ends?

CH AL L ENGE 23. Estimate the product of 742 × 423. Then, find the exact answer. Compare.

Level D

| Chapter 7 - 5

| Lighthouse MATH

151

7 - 6 | Multiplication Word Problems Round to estimate the product. 1.

DAILY REV IE W

639 × 64

870 × 13

801 × 36

L E A R N A ND C ONNEC T A farmer sells a carton of eggs for $2.25. If he sells 42 cartons, how much money will he get? We need to multiply the price of a carton by the number of cartons the farmer sells. How much does one carton cost? How many cartons did the farm sell? 2.25 42 450 + 9000 $94.50

Add the dollar sign and decimal when you finish multiplying. The farmer will make

if he sells 42 cartons of eggs.

AP P LY Read the problem. Then solve. 1. A gallon of milk costs $3.75. If a family buys 4 gallons, how much will they spend in total?

2. A bus ticket costs $2.50. If a group of 7 people each buy a ticket, what is their total cost?

3. Mr. Clark has to buy 12 textbooks for his class. Each book costs $8.50. How much money does Mr. Clark need to buy the books?

4. Larry wants to buy 20 pounds of seeds for his bakery. One pound of seeds costs $4.25. How much money will Larry have to spend?

152

Level D

| Chapter 7 - 6

| Lighthouse MATH

Exercise | 7 - 6 Name

Solve. 2. Harry picks 28 lemons off of every tree on his lemon farm. There are 30 trees on the farm. How many lemons does Harry pick?

3. Frank charges $16 for a haircut. Today, Frank gave 18 haircuts. How much money did he make?

4. Mr. Bates orders 24 pencils for each classroom in the school. There are 21 classrooms. How many pencils are ordered in total?

5. Ned is making 25 goodie bags for a party. Each bag gets 12 pieces of candy. How many pieces of candy does Ned need to fill the bags?

6. Ken practices piano for about 80 minutes a week. After 12 weeks have passed, how many minutes will Ken have practiced?

7. Sal makes 121 cookies each day. How many cookies does he make in 5 days?

8. Ella puts 142 beads on each necklace she makes. If she makes 18 necklaces, how many beads does she use?

1. Timothy studies for 60 minutes a day every day in the month of July. After 31 days, how many minutes has Timothy studied?

CH AL L ENGE 9. Baker John needs 24 pounds of apples to bake pies. Each pound of apples costs $12.25. How much money does Baker John need to buy the apples?

Level D

| Chapter 7 - 6

| Lighthouse MATH

153

7 - 7 | Chapter Review Multiply. 1.

DAILY REV IE W

947 × 10

747 × 94

134 × 76

852 × 68

L E T ' S REV I EW Multiplying by a Multiple of 10

Multiplying by Two-Digit Numbers

Put the multiple of 10 on the bottom. Write a zero, then multiply.

Multiply the ones digit in the bottom number by the top number. Write a zero. Multiply the tens digit by the top number. Add.

75 40 3,000

85 × 14 340 + 850 1,190

Rounding to Estimate Products 853 × 440

900 400 360,000

AP P LY Solve. 1.

32 × 77

61 × 97

99 × 30

77 × 89

15 × 70

96 × 33

44 × 19

23 × 33

98 10. × 75

14. 877 × 55

15. 557 × 61

11. 220 × 20

154

12. 219 × 16

Level D

13. 893 × 39

| Chapter 7 - 7

| Lighthouse MATH

84 × 47

Exercise | 7 - 7 Name

Multiply. Remember to add the dollar sign and decimal point. 1.

$5.71 × 62

$3.97 × 71

$8.79 × 25

$7.94 × 88

$6.92 × 36

$6.34 × 77

$4.77 × 80

$8.13 × 61

10. $4.89 × 89

$7.99 × 31

Round to the highest place value to estimate the answer. 11. 853 × 44

12. 78 × 78

13. 846 × 41

52 14. × 74

15. 536 × 49

69 16. × 17

17. It takes Robert 36 minutes to bake a tray of cookies. He needs to bake 12 trays of cookies in total. How many minutes will he spend baking cookies in total?

18. Gary needs to buy 15 books, one for each of his friends. Each book costs $11.50. How much money does Gary need to buy the books?

19. A small potted plant costs $5.25. If a landscaper buys 30 plants for a new garden, what is the total cost?

20. A bottle of fancy olive oil costs $8.99. If a restaurant buys 15 bottles, what is the total cost?

CH AL L ENGE 21. What is $45.26 � 84?

Level D

| Chapter 7 - 7

| Lighthouse MATH

155

Read the problem. Then solve.

7 - 8 | Cumulative Review

Solve. 1.

3 + 6

16 − 7

8 × 1

6 + 8

11 − 4

3 × 5

4 + 5

6 + 1

8 + 8

10.

1 × 4

11.

3 × 8

12.

14 − 8

13.

1 × 4

14.

4 + 3

15.

6 − 5

16.

6 − 1

17.

8 + 7

18.

1 × 7

19.

4 − 2

20.

11 − 5

21.

1 × 6

22.

3 + 5

23.

7 + 9

24.

4 × 5

25.

2 × 9

26.

1 + 1

27.

9 + 3

28.

9 × 2

29.

8 + 3

30.

14 − 6

31.

6 × 5

32.

1 + 3

33.

1 + 9

34.

5 + 9

35.

8 × 9

36.

8 − 6

37.

1 × 2

38.

12 − 3

39.

10 − 8

40.

3 + 3

41.

11 − 3

42.

8 + 5

43.

3 − 1

44.

6 × 4

45.

2 × 5

46.

7 × 2

47.

7 × 3

48.

9 − 6

49.

8 + 6

50.

8 + 1

51.

7 × 1

52.

10 − 7

53.

6 + 4

54.

2 × 3

55.

2 + 5

56.

9 + 9

57.

12 + 4

58.

14 − 6

59.

3 × 3

60.

16 − 8

61.

4 × 2

62.

8 × 2

63.

12 − 4

156

Level D

| Chapter 7 - 8

| Lighthouse MATH

Exercise | 7 - 8 Name

Add. 1.

123 + 933

352 + 193

833 + 287

3,107 + 1,964

9,465 + 8,993

7,469 + 7,649

466 − 299

865 − 351

10.

4,003 − 3,353

11.

2,002 − 1,796

12.

7,004 − 1,921

Subtract. 7.

568 − 379

Multiply. 92 × 4

14.

69 × 8

15.

14 × 3

16.

332 × 4

17.

286 × 3

18.

148 × 8

19.

56 × 95

20.

12 × 33

21.

26 × 59

22.

20 × 21

23.

752 × 41

24.

315 × 74

27.

30.

69,457

87,541

33.

326,207

362,207

13.

Write < or > to compare the numbers. 25.

352

28.

5,664

31.

49,392

26.

662

4,554

29.

4,255

58,834

32.

589,047

390

Level D

874

| Chapter 7 - 8

3,732

740,470

| Lighthouse MATH

617

157

8 C H A P T E R

158

In Chapter 8 we will learn about

Division Facts and Rules When we divide, we make equal groups. Sometimes we are looking for the number of groups, sometimes we are looking for the size of the groups. • We will draw a picture to solve division problems. • We will use multiplication facts to solve division problems. • We will learn rules for division. • We will write fact families. • We will divide by multiples of ten. • We will find remainders. • We will learn divisibility rules.

159

8 - 1 | Introduction to Division Solve. 1.

DAILY REV IE W

32 × 4

14 × 9

72 × 7

18 × 6

L E A R N A ND C ONNEC T Division helps us figure out how many are in each group or how many groups can be made. There are 24 candies. There are 4 children. How many candies can each child get? To find the answer, divide 24 into 4 groups. There are 6 in each group.

24 ÷ 4 = 6

Each child can get 6 candies.

AP P LY Fill in the correct numbers. 1.

60 Jelly Beans

How many slices per person?

60 divided by 6 = 10 60 ÷ 6 = 10 10 on each plate

Level D

divided by = 3 ÷ = 3 slices per person 4.

Every pair has 2. How many pairs? divided by ÷ = 9 pairs

160

How many on each plate?

Cars have 4 wheels. How many cars?

= 9

| Chapter 8 - 1

divided by ÷ = 4 cars

| Lighthouse MATH

= 4

Exercise | 8 - 1 Name

There are 32 plants. Use the array to answer the questions. 1. How many groups of 8? 32 ÷ 8 = 2. How many groups of 2? 32 ÷ 2 = 3. How many groups of 4? 32 ÷ 4 =

Draw a picture or an array to solve. 4. 24 ÷ 8 =

5. 9÷3=

6. 20 ÷ 5 =

7. Mark wants to buy cookies. Each cookie costs $3. He has $15. How many cookies can he buy?

Read the problem. Draw a picture or an array to solve.

CH AL L ENGE 8. If David had 12 pieces of candy, what are all the possible ways he could separate them into equal groups?

groups of groups of groups of

Level D

| Chapter 8 - 1

| Lighthouse MATH

groups of groups of groups of

161

8 - 2 | Dividing by Two and Three Fill in the missing numbers. DAILY REV IE W

×2=4

3×4=

×3=6

3×8=

L E A R N A ND C ONNEC T Count the number of shoes. Circle pairs of shoes. How many children can get a pair? There are shoes. Each child wears shoes. To find the number of children that can get a pair, divide 18 by 2.

18 ÷ 2 = 9

9 2 18

quotient

Tip!

dividend

Think: What times 2 equals 18?

divisor

There are pairs of shoes for 9 children.

AP P LY Each group is split into 2 teams. Write the number of boys on each team.

2. How many boys? How many teams? How many on each team? 8÷2=

How many boys? How many teams? How many on each team? 4÷2=

Draw a picture or an array to solve. 3.

16 ÷ 2 =

18 ÷ 3 =

9÷3=

Vocabulary Dividend - the total amount you start with in a division problem Divisor - the number you are dividing by

162

Level D

Quotient - the answer to a division problem

| Chapter 8 - 2

| Lighthouse MATH

20 ÷ 2 =

Exercise | 8 - 2 Name

18 ÷ 3 =

6÷3=

10 ÷ 2 =

4÷2=

21 ÷ 3 =

15 ÷ 3 =

12 ÷ 2 =

14 ÷ 2 =

24 ÷ 3 =

10. 8 ÷ 2 =

11. 16 ÷ 2 =

12. 12 ÷ 3 =

13. 33 ÷ 3 =

14. 21 ÷ 3 =

15. 12 ÷ 2 =

16. 6 ÷ 3 =

17. 16 ÷ 2 =

18. 3 ÷ 3 =

19. 24 ÷ 2 =

20. 16 ÷ 2 =

21. 2 8

22. 2 4

23. 3 27

24. 2 14

25. 3 24

26. 2 20

27. 2 12

28. 3 9

29. 3 15

30. 2 16

31. 3 18

32. 3 6

33. 3 9

34. 2 10

35. 3 30

36. 3 24

37. 2 2

38. 3 12

Divide.

Read the problem. Then solve. 39. A teacher has 14 books. She wants to stack them in 2 piles. How many books will be in each pile?

40. Sarah has 12 flowers. She wants to arrange them in vases, with 3 flowers in each vase. How many vases will she need?

CH AL L ENGE 41. What is 100 ÷ 2? How do you know?

Level D

| Chapter 8 - 2

| Lighthouse MATH

163

8 - 3 | Dividing by Four and Five Fill in the missing numbers. DAILY REV IE W

5×

= 20

4×2=

5×3=

× 7 = 35

L E A R N A ND C ONNEC T Count the cookies and boxes. Each box gets the same amount of cookies. How many cookies go in each box? There are cookies. There are boxes. To find the number of cookies that fit in each box, divide 20 by 5. Tip!

20 ÷ 5 = 4

Think: What times 5 equals 20?

4 5 20

4 cookies can fit in each box.

AP P LY Five pennies are equal to one nickel. Write the number of nickels equal to the pennies.

How many pennies? How many pennies in a nickel? How many nickels?

15 ÷ 5 =

20 ÷ 5 =

Draw a picture or an array to solve. 3.

164

40 ÷ 5 =

30 ÷ 5 =

Level D

| Chapter 8 - 3

8÷4=

| Lighthouse MATH

40 ÷ 4 =

Exercise | 8 - 3 Name

12 ÷ 4 =

24 ÷ 4 =

10 ÷ 5 =

8÷4=

30 ÷ 5 =

45 ÷ 5 =

25 ÷ 5 =

20 ÷ 5 =

28 ÷ 4 =

10. 35 ÷ 5 =

11. 36 ÷ 4 =

12. 20 ÷ 4 =

13. 35 ÷ 5 =

14. 18 ÷ 3 =

15. 24 ÷ 2 =

16. 12 ÷ 3 =

17. 22 ÷ 2 =

18. 2 ÷ 2 =

19. 48 ÷ 4 =

20. 50 ÷ 5 =

21. 4 32

22. 3 18

23. 3 21

24. 2 20

25. 5 15

26. 2 12

27. 5 25

28. 4 16

29. 5 30

30. 4 12

31. 2 2

32. 5 5

33. 5 10

34. 2 16

35. 4 28

36. 2 6

37. 2 4

38. 2 8

Divide.

Read the problem. Then solve. 39. A baker made 25 cookies. He wants to give them to 5 friends, with each person getting an equal amount of cookies. How many cookies does each friend receive?

40. There are 36 people waiting to ride a small amusement park ride. Each car on the ride holds 4 people. How many cars will be filled?

CH AL L ENGE 41. I have 40 coins. I divide them into 4 piles. Then, I give away 5 coins from each pile. How many coins do I have left in each pile?

Level D

| Chapter 8 - 3 | Lighthouse MATH

165

8 - 4 | Dividing by Six and Seven Fill in the missing numbers. DAILY REV IE W

6×9=

7×

= 35

7×

= 28

7×8=

L E A R N A ND C ONNEC T Count the beads and strings. If the same number of beads are strung on each string, how many beads will be on each bracelet? There are beads. There are strings. To find the number of beads on each bracelet, divide 54 by 6. Tip!

54 ÷ 6 = 9

Think: What times 6 equals 54?

9 6 54

Each bracelet will have 9 beads.

AP P LY

Danny spends the same amount each day, for 7 days. How many dollars did he spend each day? 1.

How many dollars? How many days? How many per day?

21 ÷ 7 =

14 ÷ 7 =

Draw a picture or an array to solve. 3.

166

48 ÷ 6 =

36 ÷ 6 =

Level D

| Chapter 8 - 4

42 ÷ 6 =

| Lighthouse MATH

70 ÷ 7 =

Exercise | 8 - 4 Name

24 ÷ 6 =

54 ÷ 6 =

14 ÷ 7 =

18 ÷ 6 =

42 ÷ 7 =

56 ÷ 7 =

63 ÷ 9 =

21 ÷ 7 =

7÷7=

10. 12 ÷ 6 =

11. 30 ÷ 6 =

12. 28 ÷ 7 =

13. 36 ÷ 6 =

14. 60 ÷ 6 =

15. 8 ÷ 2 =

16. 14 ÷ 7 =

17. 6 ÷ 6 =

18. 28 ÷ 7 =

19. 21 ÷ 7 =

20. 24 ÷ 3 =

21. 5 20

22. 2 2

23. 7 14

24. 3 24

25. 2 6

26. 7 7

27. 6 36

28. 7 21

29. 3 30

30. 4 24

31. 7 63

32. 4 20

33. 3 6

34. 5 35

35. 6 54

36. 5 5

37. 6 18

38. 4 12

Read the problem. Then solve. 39. A class of 30 students needs to form 6 equal groups for a project. How many students will be in each group?

40. There are 56 people waiting to ride a small train. Each car on the train holds 7 people. How many cars will be filled?

CH AL L ENGE 41. Solve the riddle. When I am divided by 6, the result is the same as when 5 is added to the number 2. What number am I?

Level D

| Chapter 8 - 4

| Lighthouse MATH

167

Divide.

8 - 5 | Dividing by Eight and Nine Fill in the missing numbers. DAILY REV IE W

8×7=

8×

= 48

9×

= 72

9×

L E A R N A ND C ONNEC T Count the number of pizza slices. Each pie had 8 slices. How many pies were there? There were 24 slices. Each pizza had 8 slices. To find the number of pies, divide 24 by 8. Tip!

24 ÷ 8 = 3

3 8 24

Think: What times 8 equals 24?

There were 3 pies.

AP P LY 9 muffins can fit in each box. Write the number of boxes needed.

How many muffins? How many in each box? How many boxes? 27 ÷ 9 =

Draw a picture or an array to solve. 3.

168

64 ÷ 8 =

54 ÷ 9 =

Level D

| Chapter 8 - 5

56 ÷ 8 =

| Lighthouse MATH

9÷9=

= 36

Exercise | 8 - 5 Name

18 ÷ 9 =

81 ÷ 9 =

16 ÷ 8 =

64 ÷ 8 =

48 ÷ 8 =

27 ÷ 9 =

72 ÷ 9 =

54 ÷ 9 =

32 ÷ 8 =

10. 72 ÷ 8 =

11. 36 ÷ 9 =

12. 40 ÷ 8 =

13. 48 ÷ 8 =

14. 8 ÷ 8 =

15. 81 ÷ 9 =

16. 63 ÷ 9 =

17. 9 ÷ 1 =

18. 28 ÷ 7 =

19. 9 ÷ 3 =

20. 20 ÷ 4 =

21. 3 9

22. 3 6

23. 6 24

24. 9 27

25. 3 27

26. 5 25

27. 7 42

28. 8 80

29. 3 24

30. 3 18

31. 4 28

32. 6 30

33. 8 64

34. 9 45

35. 9 90

36. 2 4

37. 2 8

38. 3 3

Divide.

Read the problem. Then solve. 39. There are 40 cookies to share equally among 8 children. How many cookies does each child get?

40. A garden has 63 roses arranged in rows and columns. If there are 9 roses in each row, how many columns are there?

CH AL L ENGE 41. If 32 divided by 8 is 4, what is 32 divided by 16?

Level D

| Chapter 8 - 5

| Lighthouse MATH

169

8 - 6 | Dividing by Zero and One Divide. DAILY REV IE W

7 42

8 48

6 24

5 40

L E A R N A ND C ONNEC T Any number divided by itself equals 1.

Any number divided by 1 equals itself.

There are 4 slices.

There are 4 plates.

There is 1 plate.

Each plate has 1 slice.

Each plate has 4 slices.

4÷4=1 4×1=4

4÷1=4 1×4=4

0 divided by any number equals 0.

You cannot divide by 0.

There are 0 slices.

There are 4 slices.

There are 4 plates.

There are 0 plates.

Each plate has 0 slices.

0÷4=0 4×0=0

4÷0=? 0×?=4

AP P LY Write the number of roses in each vase. 1.

How many roses? How many vases? How many roses in each vase? 2÷1=

170

Level D

How many roses? How many vases? How many roses in each vase? 2÷2=

| Chapter 8 - 6

| Lighthouse MATH

Exercise | 8 - 6 Name

2÷2=

8÷1=

4÷4=

8÷8=

1÷1=

0÷7=

0÷8=

12 ÷ 1 =

2÷1=

10. 10 ÷ 1 =

11. 0 ÷ 5 =

12. 0 ÷ 11 =

13. 3 ÷ 3 =

14. 4 ÷ 0 =

15. 7 ÷ 7 =

16. 0 ÷ 10 =

17. 0 ÷ 4 =

18. 2 ÷ 0 =

19. 10 ÷ 0 =

20. 6 ÷ 6 =

21. 2 0

22. 6 36

23. 6 12

24. 9 54

25. 4 28

26. 4 36

27. 6 6

28. 8 80

29. 6 24

30. 8 56

31. 3 21

32. 9 0

33. 6 54

34. 1 10

35. 6 42

36. 5 10

37. 7 42

38. 4 16

Read the problem. Then solve. 39. There is a group of 5 friends who have a bag of 5 muffins. How many muffins does each friend get if they share them equally?

40. Water bottles cost $2. How many water bottles can a person buy with $0?

CH AL L ENGE 41. Use a multiplication fact to explain why you cannot divide by 0.

Level D

| Chapter 8 - 6

| Lighthouse MATH

171

Divide.

8 - 7 | Multiplication and Division Fact Families Divide. DAILY REV IE W

9 36

9 54

6 42

2 14

L E A R N A ND C ONNEC T A fact family is a group of two multiplication facts and two division facts with the same numbers.

6, 9, 54

6 × 9 = 54 9 × 6 = 54

54 ÷ 9 = 6 54 ÷ 6 = 9

6 × 9 = 54 9 × 6 = 54

54 ÷ 9 = 6 54 ÷ 6 = 9

AP P LY

Write the fact family. 1. 21, 3, 7

2. 12, 3, 4

3. 20, 4, 5

4. 30, 5, 6

5. 42, 6, 7

6. 56, 7, 8

7. 72, 8, 9

8. 100, 10, 10

Vocabulary Product - the answer to a multiplication problem Math facts - basic number sentences Fact family - a group of related math facts

172

Level D

| Chapter 8 - 7

| Lighthouse MATH

Exercise | 8 - 7 Name

Write the fact family. 1. 8, 2, 4

2. 15, 3, 5

3. 18, 2, 9

4. 28, 4, 7

5. 32, 4, 8

6. 5, 2, 10

7. 18, 3, 6

8. 40, 5, 8

9. 48, 6, 8

10. 27, 3, 9

Find the missing number in the fact family. 12. 8 ÷ 4 = 2

5×

4×

= 30

15. 12 ÷ 4 = 3

17. 40 ÷ 8 = 5

= 56

8×

÷6=2 23. 8 × 8 = 64 =8

21. 10 × 5 = 50

8÷

÷ 5 = 10

24. 4 × 3 = 12

25. 5 × 9 = 45

÷3=4

× 8 = 24 18. 32 ÷ 8 = 4

× 8 = 40

20. 2 × 4 = 8

19. 2 × 6 = 12

14. 24 ÷ 8 = 3

× 7 = 28

16. 56 ÷ 8 = 7

× 4 = 12

64 ÷

13. 28 ÷ 7 = 4

8×

= 32 © Lighthouse Curriculum. Copying strictly prohibited.

11. 30 ÷ 5 = 6

22. 5 × 3 = 15 15 ÷

26. 5 × 7 = 35

÷9=5

÷7=5

CH AL L ENGE Find the missing number in the fact family. 27. 81 ÷

28. 144 ÷

Level D

| Chapter 8 - 7

= 12

| Lighthouse MATH

173

8 - 8 | Solving Division with Multiplication Fill in the missing numbers. DAILY REV IE W

×2=4

3×4=

×4=8

3×8=

L E A R N A ND C ONNEC T Division is the opposite of multiplication. When we divide, we create equal groups.

18 ÷ 3

3 18

18 divided by 3 We can use a multiplication fact to help us divide. Think

Solve

What times 3 equals 18?

18 ÷ 3 = 6

3 × 6 = 18

6 3 18

AP P LY Fill in the missing number. 1. 15 ÷ 3 = 5 3 × 5 = 15

5. 25 ÷ 5 = 5×

174

2. 16 ÷ 2 = 2×

3. 12 ÷ 3 = = 16

6. 2 ÷ 2 = = 25

3×

4. 20 ÷ 4 = = 12

7. 9 ÷ 3 =

2×

Level D

| Chapter 8 - 8

3×

4×

= 20

8. 8 ÷ 4 = =9

| Lighthouse MATH

4×

Exercise | 8 - 8 Name

Fill in the missing number. 1.

8 × 7 = 56

× 4 = 20

× 6 = 24

× 5 = 40

× 7 = 63

× 6 = 54

8×

= 48

10.

× 5 = 35

11. 6 ×

= 36

12.

13. 9 ×

= 63

14.

× 6 = 18

15. 9 ×

= 18

16. 6 ×

= 30

= 24

19. 7 ×

= 28

20. 4 ×

= 28

× 10 = 20

23. 4 ×

= 32

24.

17.

21. 6 ×

18. 8 ×

× 7 = 21

22.

= 18

×4=8

3×

= 27

× 8 = 64

× 7 = 49

Circle the equation that can be used to solve the division problem. 26. 54 ÷ 9 = 6

2×

= 18

2 × 18 =

54 ×

27. 40 ÷ 8 = 40 × 8 = 40

25. 18 ÷ 2 = 9

× 6 = 54

28. 28 ÷ 4 = 7 40 × 8 =

4 × 28 =

4×

= 28

CH AL L ENGE 29. If you know that 12 ÷ 4 = 3, what other multiplication and division problems do you know the answers to?

Level D

| Chapter 8 - 8

| Lighthouse MATH

175

8 - 9 | Dividing by Multiples of 10 Multiply. DAILY REV IE W

8×8=

3×3=

6×4=

9×7=

L E A R N A ND C ONNEC T To divide by a multiple of ten, cross out the same number of zeros from both numbers. Divide the numbers without the zeros. Add the number of zeros left to your answer. Cross out the same number of zeros from both numbers.

Divide the numbers without the zeros. 15 ÷ 5 = 1,50 ÷ 5 = 15,00 ÷ 5 = 150,00 ÷ 5 =

150 ÷ 50 = 1,500 ÷ 50 = 15,000 ÷ 50 = 150,000 ÷ 50 =

Add the zeros left to the end of the answer.

3 3 3 3

15 ÷ 5 = 1,50 ÷ 5 = 15,00 ÷ 5 = 150,00 ÷ 5 =

3 30 300 3,000

AP P LY Use patterns to divide.

176

270 ÷ 10 =

560 ÷ 10 =

470 ÷ 10 =

2,700 ÷ 10 =

5,600 ÷ 10 =

4,700 ÷ 10 =

27,000 ÷ 10 =

56,000 ÷ 10 =

47,000 ÷ 10 =

270,000 ÷ 10 =

560,000 ÷ 10 =

470,000 ÷ 10 =

640 ÷ 80 =

480 ÷ 60 =

630 ÷ 90 =

6,400 ÷ 80 =

4,800 ÷ 60 =

6,300 ÷ 90 =

64,000 ÷ 80 =

48,000 ÷ 60 =

63,000 ÷ 90 =

640,000 ÷ 80 =

480,000 ÷ 60 =

630,000 ÷ 90 =

Level D

| Chapter 8 - 9

| Lighthouse MATH

Exercise | 8 - 9 Name

420 ÷ 6 =

150 ÷ 3 =

630 ÷ 90 =

800 ÷ 20 =

2,400 ÷ 80 =

3,500 ÷ 50 =

4,800 ÷ 60 =

1,200 ÷ 40 =

18,000 ÷ 20 =

10. 27,000 ÷ 30 =

11. 45,000 ÷ 500 =

12. 81,000 ÷ 90 =

13. 72,000 ÷ 800 =

14. 24,000 ÷ 6,000 =

15. 14,000 ÷ 70 =

16. 36,000 ÷ 900 =

17. 120,000 ÷ 30 =

18. 280,000 ÷ 40 =

19. 500,000 ÷ 50 =

20. 180,000 ÷ 900 =

21. 360 ÷ 4 =

22. 210 ÷ 70 =

23. 32,000 ÷ 4,000 =

24. 16,000 ÷ 80 =

25. 5,400 ÷ 900 =

26. 4,000 ÷ 80 =

27. 25,000 ÷ 50 =

28. 8,000 ÷ 40 =

29. 480,000 ÷ 60 =

30. 540 ÷ 90 =

Divide.

Read the problem. Then solve. 31. A factory produces 800 bottles of soda per hour. If they are packed into cases of 20 bottles, how many cases can they fill in an hour?

32. An airline has to transport 36,000 passengers. If each plane holds 90 passengers, how many planes are needed?

CH AL L ENGE 33. What is 40,000,000 ÷ 500?

Level D

| Chapter 8 - 9

| Lighthouse MATH

177

8 - 10 | Equal Groups with Some Left Over Divide. DAILY REV IE W

6 48

2 16

6 18

9 81

L E A R N A ND C ONNEC T 20 candies are shared equally with 3 children. How many does each child get? How many are left over? Each child gets 6 candies. There are 2 candies left over. The amount left over is called the remainder. The remainder is 2.

AP P LY

Circle equal groups. Write how many groups or how many in each. Write how many are left over. 1.

Each shirt needs 5 buttons. How many shirts? How many left over?

Taffies divided equally into 4 bags How many in each bag? How many left over?

4. Blocks are shared equally between 3 children. How many does each child get? How many left over?

Each letter needs 2 stamps. How many letters? How many left over?

Vocabulary Remainder - the amount left over when dividing

178

Level D

| Chapter 8 - 10

| Lighthouse MATH

Exercise | 8 - 10 Name

Make equal groups. Write how many are left over. 1.

34 Jelly Beans

How many on each plate?

How many slices per person?

How many pairs?

How many are left over?

How many without a pair?

Draw a picture to answer the question. 5. 5 sticker sheets each have the same amount of stickers. There are 43 stickers in all.

How many painters?

How many on each sheet?

How many are left over?

Draw a picture. Then solve. 6. Each beach ball costs $7. How many beach balls can you buy with $18? How much money will you have left over?

beach balls $

left over

CH AL L ENGE with

left over

8. 19 ÷ 6 =

75 ÷ 9 =

with

left over

11. 58 ÷ 7 =

with

left over

7. 23 ÷ 3 = 9.

Level D

| Chapter 8 - 10

with

left over

10. 36 ÷ 5 =

with

left over

12. 17 ÷ 3 =

with

left over

| Lighthouse MATH

179

4. There are 50 paintbrushes. Each painter needs 6.

8 - 11 | Divisibility Rules Divide. DAILY REV IE W

8 32

7 56

7 14

6 12

L E A R N A ND C ONNEC T Use these rules to know if a number can be divided without any left over.

A number is divisible by...

if it ends with 0, 2, 4, 6, or 8.

if it equals 3, 6, or 9 when you add up all its digits. If it has more than one digit, add the digits again.

if it ends with a 0 or a 5.

if it equals 9 when you add up all its digits. If it has more than one digit, add the digits again.

if it ends with a 0.

AP P LY What numbers can 36 be divided by with none left over? 1.

Does 36 end with 0, 2, 4, 6, or 8?

Is 36 divisible by 2?

Does 36 equal 3, 6, or 9 when you add up all its digits?

Is 36 divisible by 3?

Does 36 end with a 0 or a 5?

Is 36 divisible by 5?

Does 36 equal 9 when you add up all its digits?

Is 36 divisible by 9?

Does 36 end with a 0?

Is 36 divisible by 10?

Vocabulary Divisible - can be divided without any left over

180

Level D

| Chapter 8 - 11

| Lighthouse MATH

Exercise | 8 - 11 Name

10. 21

11. 82

12. 41

13. 15

14. 35

15. 70

16. 81

For each number, circle the number or numbers it is divisible by. Hint: There may be no correct numbers to circle.

Read the problem. Then solve. 17. There are 50 members in the choir. Can they line up in 2, 3, 5, 9, or 10 equal rows? List all the possibilities.

18. Jeff has 36 books. He wants to place them on shelves in equal numbers. Can he place them on 2, 3, 5, 9, or 10 shelves? List all the possibilities.

CH AL L ENGE 19. Any number that is divisible by 10 is also divisible by 2 and 5. Can you explain why?

Level D

| Chapter 8 - 11

| Lighthouse MATH

181

8 - 12 | Chapter Review Divide. DAILY REV IE W

5÷1=

8÷2=

48 ÷ 8 =

36 ÷ 9 =

L E T ' S REV I EW Division Facts

Division Properties and Rules

When we divide, we create equal groups. Use a multiplication fact to solve division.

A number divided by 1 equals itself. A number divided by itself equals 1. 0 divided by a number equals 0.

40 ÷ 8 = 5

You cannot divide by 0.

Think: What times 8 equals 40?

Dividing by Multiples of 10

Remainders

Cross out the same number of zeros from both numbers. Divide the numbers without the zeros. Add the number of zeros left to your answer.

Sometimes, when we divide we have some leftover. We can use divisibility rules to know if there will be a remainder. 17 stickers on 3 pages

2,500 ÷ 50 = 50

5 stickers are on each page with 2 left over.

AP P LY Divide. 1.

7÷1=

63 ÷ 9 =

32 ÷ 4 =

3÷3=

36 ÷ 4 =

24 ÷ 4 =

72 ÷ 8 =

30 ÷ 6 =

8 48

15. 1 8

182

10. 6 54

11. 2 12

12. 2 16

13. 2 10

14. 6 42

16. 4 36

17. 9 90

18. 7 28

19. 5 5

20. 7 63

Level D

| Chapter 8 - 12

| Lighthouse MATH

Exercise | 8 - 12 Name

Divide. 1.

5÷5=

12 ÷ 2 =

21 ÷ 3 =

81 ÷ 9 =

24 ÷ 3 =

21 ÷ 7 =

28 ÷ 4 =

9÷1=

16 ÷ 2 =

10. 7 ÷ 7 =

11. 15 ÷ 3 =

12. 63 ÷ 7 =

13. 6 18

14. 7 49

15. 9 72

16. 3 21

17. 1 4

18. 7 42

19. 5 30

20. 2 20

21. 1 9

22. 5 45

23. 6 48

24. 6 36

25. 5 25

26. 4 32

27. 8 56

28. 9 18

29. 7 70

30. 2 14

Write how many are left over. 32. 24 children divided into teams of 5.

How many pages?

How many teams?

How many are left over?

Read the problem. Then solve. 33. A group of 5 friends paid $25 for a pizza. They want to split the cost evenly. How much does each person have to pay?

34. Emily has $18. She wants to buy toy cars that cost $3 each. How many toy cars can she buy?

cars

CH AL L ENGE 35. If you divide me by 7, the answer is a whole number. If you divide me by 2, you also get a whole number. My number is between 20 and 30. What number am I?

Level D

| Chapter 8 - 12

| Lighthouse MATH

183

31. 34 stickers with 6 stickers on each page.

8 - 13 | Cumulative Review

Solve. 1.

4 + 4

3 + 1

5 × 3

3 × 8

6 − 4

1 + 8

12 − 9

8 × 5

4 + 1

10.

8 + 3

11.

8 + 5

12.

6 × 5

13.

16 − 9

14.

17 − 9

15.

7 + 3

16.

5 + 7

17.

6 + 7

18.

7 × 5

19.

11 − 6

20.

1 + 5

21.

14 − 8

22.

6 − 2

23.

9 + 6

24.

4 + 6

25.

14 − 5

26.

10 − 3

27.

8 + 7

28.

4 × 7

29.

9 × 9

30.

3 × 1

31.

7 × 7

32.

13 − 9

33.

7 − 1

34.

3 + 3

35.

5 + 4

36.

4 × 3

37. 7 63

38. 4 36

39. 8 8

40. 5 20

41. 2 16

42. 6 42

43. 9 18

44. 2 12

45. 8 56

46. 9 81

47. 4 28

48. 2 10

49. 7 42

50. 6 36

51. 6 42

52. 6 48

53. 5 30

54. 5 50

184

Level D

| Chapter 8 - 13

| Lighthouse MATH

Exercise | 8 - 13 Name

Add. 1.

951 + 263

986 + 848

280 + 372

7,540 + 1,648

9,569 + 6,258

6,765 + 2,954

606 − 457

825 − 736

10.

2,324 − 1,663

11.

2,891 − 151

12.

4,232 − 432

14.

98 × 8

15.

571 × 7

16.

694 × 3

17.

14 × 90

18.

83 × 82

Subtract. 7.

774 − 645

Multiply. 13.

12 × 7

Divide. 20. 5 40

24. 7 28

23. 4 36

22. 6 36

21. 8 64

Add or subtract. 25.

$76.89 − $29.40

26.

$61.69 + $37.22

27.

$62.21 + $5.42

28.

$74.11 + $13.60

29.

$88.48 − $70.65

30.

$63.97 − $1.87

31.

$12.79 + $85.52

32.

$59.90 − $53.55

33.

$75.09 + $23.30

34.

$48.43 + $34.74

Level D

| Chapter 8 - 13

| Lighthouse MATH

185

19. 5 30

9 C H A P T E R

186

In Chapter 9 we will learn about

Long Division When we divide large numbers, we follow a set of steps to make dividing easier. We work on the numbers from left to right. • We will divide with remainders. • We will learn how to check division problems with remainders. • We will learn the steps of long division. • We will interpret remainders.

187

9 - 1 | Dividing with Remainders The same amount goes in each sack. Write the amount in each sack and the amount left over. in each sack

DAILY REV IE W

left over

L E A R N A ND C ONNEC T Mark has $19 to spend on potato chips. Each bag costs $3. How many bags can he buy? How much money will he have left over? To find the number of bags, divide by . The amount of money left over is called the remainder. D Divide.

M Multiply.

S Subtract.

R Remainder.

6 3 19

6 3 19 18

6 3 19 − 18 1

6 R1 3 19 − 18 1

19 − 18 = 1 Make sure 1 < 3

Write the remainder (the amount left over).

How many times does 3 fit into 19?

6 × 3 = 18

3 × 6 = 18 3 × 7 = 21

The remainder must always be less than the divisor.

It fits 6 times.

Mark can buy 6 bags with $1 left over.

AP P LY Fill in the missing numbers. 1.

R 8 5 8 −

R 3 2 5 −

R 4 3 4 −

Vocabulary Remainder - the amount left over in a division problem

188

Level D

| Chapter 9 - 1

| Lighthouse MATH

R 7 5 3 −

Exercise | 9 - 1 Name

Divide. 1.

7 21

8 20

2 18

3 13

8 47

2 12

4 14

5 31

10. 7 32

14. 4 6

15. 7 37

11. 5 52

12. 2 9

13. 8 36

5 41

16. 50 ÷ 9

17. 30 ÷ 9

18. 53 ÷ 6

19. 37 ÷ 6

20. 51 ÷ 7

21. 38 ÷ 4

22. 22 ÷ 3

23. 34 ÷ 6

Read the problem. Then solve. 24. A baker has 17 cookies to put into bags. Each bag can hold 5 cookies. How many full bags of cookies can the baker make? How many cookies will be left over?

25. A gardener has 19 flowers to plant in rows. Each row can hold 6 flowers. How many full rows can the gardener plant? How many flowers will be left over?

CH AL L ENGE 26. Each container holds 6 eggs. How many containers are needed for 25 eggs?

Level D

| Chapter 9 - 1

| Lighthouse MATH

189

Rewrite and divide.

9 - 2 | Checking Division Divide. DAILY REV IE W

9 66

8 45

7 18

8 62

L E A R N A ND C ONNEC T To check division, multiply the divisor by the quotient. Then, add any remainder. If the sum is the same as the dividend, the answer is correct.

Divide quotient

Check remainder

4 R5 8 37 − 32 5 dividend

divisor

8 × 4 32

32 + 5 37

I f the sum is the same as the dividend, the answer is correct.

AP P LY

Fill in the missing numbers. Check your work. 1.

Check:

R 9 7 3 −

Check:

6 5 2 −

5 +

Check:

R 5 4 7 −

4 2 6 −

4 ×

Vocabulary Dividend - the starting amount in a division problem Divisor - the number you divide by in a division problem

190

Level D

Quotient - the answer to a division problem Remainder - the amount left over in a division problem

| Chapter 9 - 2

| Lighthouse MATH

Exercise | 9 - 2 Name

Divide. Check your work. 1.

5 29

6 50

6 20

Check:

9 69

7 69

7 8

Check:

5 16

2 15

9 57

Check:

10. 78 ÷ 8

11. 44 ÷ 5

12. 47 ÷ 6

13. 51 ÷ 6

14. 23 ÷ 4

15. 22 ÷ 4

16. 36 ÷ 7

17. 57 ÷ 7

Rewrite and divide.

Read the problem. Then solve. Check your work. 18. A teacher has 50 new pencils. She wants to divide them equally among 6 student groups. How many pencils will each group get, and how many pencils will be left over?

CH AL L ENGE 19. A caterer has 46 mini-muffins and wants to put them onto trays that hold 7 muffins each. How many trays does he need? Explain.

Level D

| Chapter 9 - 2

| Lighthouse MATH

191

9 - 3 | Long Division Divide. DAILY REV IE W

5 42

9 42

5 14

2 5

L E A R N A ND C ONNEC T Mr. Stewart is stocking apples at the supermarket. He has 72 apples to place in 6 rows. How many apples can he put in each row? To find how many apples will be in each row, we divide

Divide the tens.

Divide the ones.

1 6 72 − 6 1

1 6 72 − 6 12

12 6 72 − 6 12 − 12 0

D Divide

6 fits into 7: 1 time

B B ring Down

D Divide

6 fits into 12: 2 times

M Multiply

1×6=6

he ones T digit (2)

M Multiply

2 × 6 = 12

S Subtract 7 − 6 = 1

S Subtract 12 − 12 = 0

Make sure 1 < 6

Make sure 0 < 6

R Remainder There are 0 left over

(no remainder)

He can put 12 apples in each row.

AP P LY Divide. 1.

192

3 6 3 −

5 6 0 −

7 9 8 −

2 6 4 −

2 7 2 −

−

Level D

| Chapter 9 - 3

| Lighthouse MATH

Exercise | 9 - 3 Name

Divide. 1.

3 69

4 84

2 86

3 93

2 58

3 57

5 65

4 76

10. 2 46

14. 3 66

15. 2 98

11. 3 96

12. 2 62

13. 2 38

2 70

Rewrite and divide. 17. 42 ÷ 3

18. 94 ÷ 2

19. 66 ÷ 2 © Lighthouse Curriculum. Copying strictly prohibited.

16. 26 ÷ 2

Read the problem. Then solve. 20. A carpenter has a piece of wood that is 72 inches long. He needs to cut it into 3-inch sections. How many 3-inch sections can he cut?

21. A farmer picks 65 apples and wants to put 5 apples into each bag. How many bags can he fill?

CH AL L ENGE 22. What is 99 ÷ 7?

Level D

| Chapter 9 - 3

| Lighthouse MATH

193

9 - 4 | Long Division with Remainders Divide. DAILY REV IE W

60 ÷ 5 =

86 ÷ 2 =

88 ÷ 4 =

57 ÷ 3 =

L E A R N A ND C ONNEC T There are 59 mini cookies. 4 friends want to share them so each of them gets the same amount. How many cookies can each friend get? How many will be left over? To find out how many cookies each person can get and how many are left over, we divide

Divide the tens.

Divide the ones.

1 4 59 − 4 1

4 fits into 5: 1 time

D Divide

B Bring Down

1×4=4

M Multiply

D Divide

4 fits into 19: 4 times

M Multiply

4 × 4 = 16

he ones T digit (9)

S Subtract 5 − 4 = 1

Make sure 1 < 4

14 R3 4 59 − 4 19 − 16 3

1 4 59 − 4 19

S Subtract 19 − 16 = 3

Make sure 3 < 4

R Remainder There are 3 left over.

Each friend can get 14 cookies with 3 cookies left over.

AP P LY Divide. 1.

194

5 6 2 −

3 7 4 −

4 9 1 −

3 5 5 −

−

Level D

| Chapter 9 - 4

| Lighthouse MATH

Exercise | 9 - 4 Name

Divide. 1.

4 62

2 53

5 58

3 94

2 97

3 79

5 62

7 78

10. 8 97

14. 6 94

15. 2 73

11. 5 91

12. 3 82

13. 4 45

2 57

Rewrite and divide. 17. 73 ÷ 2

18. 99 ÷ 5

19. 39 ÷ 4

Read the problem. Then solve. 20. A gardener grew 50 carrots. He wants to bundle them into groups of 8. How many full bundles can he make? How many carrots will be left over?

21. You have 35 balloons and want to give 6 balloons to each of your friends. How many friends can receive a full set of balloons? How many balloons will be left over?

CH AL L ENGE 22. A librarian has 45 books. Each shelf can hold a maximum of 7 books. If the librarian only wants full shelves, how many more books would she need to buy?

Level D

| Chapter 9 - 4

| Lighthouse MATH

195

16. 94 ÷ 6

9 - 5 | Understanding Remainders Fill in the missing number. DAILY REV IE W

86 ÷ 7 =

90 ÷ 8 =

83 ÷ 2 =

44 ÷ 3 =

L E A R N A ND C ONNEC T There are 75 guests. Each table seats 6 people. How many tables are needed for all the guests? To find the number of tables, we divide by . 12 R3 6 75 − 6 15 − 12 3

Tip!

There will be 12 full tables. Since there will be another 3 guests at a table that is not full, 13 tables will be needed.

Sometimes, the remainder affects the answer, and sometimes, it does not.

AP P LY Solve each problem. 1. A company needs to ship 86 shirts. They can fit 7 shirts in each shipping box. How many boxes are needed to ship all of the shirts?

2. A seamstress has a roll of fabric that is 47 feet long. She needs 3 feet of fabric to make one dress. How many dresses can she make?

3. A box of markers costs $8. How many boxes can you buy with $94?

4. A chef needs to buy 99 lemons. The lemons come in packages of 8. How many packages does he need to buy?

196

Level D

| Chapter 9 - 5

| Lighthouse MATH

Exercise | 9 - 5 Name

Divide. 1.

3 40

6 70

5 57

3 88

6 85

2 49

5 75

7 88

10. 3 51

14. 7 87

15. 3 77

11. 3 67

12. 2 98

13. 4 78

5 65

16. A warehouse needs to move 74 large carpets. Their forklift can only move 3 carpets at a time. How many trips does the forklift have to make to move all the carpets?

Read the problem. Then solve. 17. Ilana makes $5 an hour babysitting. She needs $68 to buy a new art set. How many hours does she need to babysit to pay for the art set?

CH AL L ENGE 18. Each muffin tray holds 6 muffins. A baker fills 7 full trays plus one tray with 4 muffins. How many muffins did she make?

Level D

| Chapter 9 - 5

| Lighthouse MATH

197

9 - 6 | Chapter Review Divide. DAILY REV IE W

4 49

2 99

8 91

3 98

L E T ' S REV I EW Long division

Understanding the Remainder

34 R2 6 206 − 18 26 − 24 2

Jack has to ship 206 jars of jam. If he puts 6 jars into each box he packs, how many boxes will he need? 34 R2 6 206

D Divide

6 fits into 20: 3 times

M Multiply

3 × 6 = 18

He will pack

S Subtract 20 − 18 = 2

In total, Jack needs

Make sure 2 < 6

B Bring Down

the ones digit (6)

D Divide

6 fits into 26: 4 times

M Multiply

6 × 4 = 24

boxes.

Checking Division

S Subtract 26 − 24 = 2

34 × 6 204

Make sure 2 < 6

R Remainder There are 2 left over. © Lighthouse Curriculum. Copying strictly prohibited.

full boxes and one box jars. with

204 2 206

AP P LY Divide. 1.

198

3 7 6 −

2 6 2 −

−

R 4 1 9 −

R 3 8 −

5. 3 8 4 − −

Level D

| Chapter 9 - 6

| Lighthouse MATH

Exercise | 9 - 6 Name

Divide. 1.

3 50

3 45

9 23

2 68

5 43

5 87

10. 8 61

4 92

3 55

11. 4 22

9 29

12. 9 24

Rewrite and divide. 13. 88 ÷ 6

14. 92 ÷ 8

15. 52 ÷ 4

16. 44 ÷ 2

17. 25 ÷ 3

18. A 55-foot roll of ribbon is used to wrap presents. Each present uses 3 feet of ribbon. After wrapping as many presents as possible, how many feet of ribbon are left over?

19. A child has a box with 89 Lego bricks and wants to build towers that are 7 bricks tall. How many complete towers can they build?

CH AL L ENGE 20. A baker has 50 cups of flour. A large cake recipe requires 7 cups of flour, and a small cake recipe requires 4 cups. How many large and small cakes could the baker make without having leftover flour?

Level D

| Chapter 9 - 6

| Lighthouse MATH

199

Read the problem. Then solve.

9 - 7 | Cumulative Review

Solve. 1.

12 − 7

10 − 5

4 × 7

5 + 2

7 + 6

1 × 7

8 × 1

6 × 8

1 + 1

10.

8 × 3

11.

8 + 7

12.

2 × 5

13.

12 − 8

14.

8 + 4

15.

3 × 8

16.

6 − 4

17.

8 + 6

18.

8 × 4

19.

6 − 1

20.

10 − 6

21.

1 × 9

22.

5 − 2

23.

16 − 7

24.

4 + 9

25.

6 + 6

26.

10 − 8

27.

9 − 1

28.

6 × 5

29.

8 × 2

30.

2 × 6

31.

4 × 6

32.

11 − 5

33.

8 − 5

34.

6 + 3

35.

1 × 8

36.

6 − 2

37. 6 36

38. 5 30

39. 9 81

40. 7 49

41. 6 18

42. 3 21

43. 5 10

44. 1 7

45. 4 12

46. 3 12

47. 2 14

48. 3 36

49. 7 56

50. 6 48

51. 6 12

52. 5 25

53. 4 32

54. 8 64

200

Level D

| Chapter 9 - 7

| Lighthouse MATH

Exercise | 9 - 7 Name

Add. 1.

519 + 762

829 + 132

311 + 478

7,129 + 9,303

3,339 + 2,230

2,025 + 4,567

685 − 333

517 − 275

10.

9,705 − 6,053

11.

9,162 − 3,133

12.

9,650 − 2,192

14.

22 × 4

15.

350 × 3

16.

118 × 3

17.

51 × 66

18.

31 × 63

Subtract. 7.

851 − 234

Multiply. 13.

71 × 8

Divide. 24. 2 39

23. 4 50

22. 3 93

For each number, circle the number or numbers it is divisible by. Hint: There may be no correct numbers to circle. 25. 32

26. 20

27. 45

28. 29

29. 27

30. 15

31. 17

32. 34

33. 60

34. 40

Level D

| Chapter 9 - 7

| Lighthouse MATH

201

21. 4 38

20. 2 11

19. 7 43

10 C H A P T E R

202

In Chapter 10 we will learn more about

Long Division (Continued) When dividing larger numbers, we use place value to divide. We follow the steps of long division to keep our work organized. • We will divide three and four-digit numbers with and without remainders. • We will learn how to divide when 0 is part of the quotient. • We will learn how to figure out where to start dividing. • We will learn how to divide money.

203

10 - 1 | Three-Digit Dividends Divide. DAILY REV IE W

5 82

2 76

2 94

5 16

L E A R N A ND C ONNEC T Dennis and his brother Ben will paddle their boat 486 feet across a pond. What is the length of the pond in yards? Hint: There are 3 feet in a yard. To find out how many yards the pond is, divide by . Divide the hundreds. 1 3 486 − 3 18

Divide the tens. 16 3 486 − 3 18 − 18 06

D Divide 3 fits into 4:

Divide the ones. 162 3 486 − 3 18 − 18 06 − 06 0

D Divide 3 fits into 18:

1 time M Multiply 1×3=3 S Subtract 4−3=1 Make sure 1 < 3 B Bring down The tens digit (8)

D Divide 3 fits into 6:

6 times M Multiply 6 × 3 = 18 S Subtract 18 − 18 = 0 Make sure 0 < 3 B Bring down The ones digit (6)

2 times M Multiply 2×3=6 S Subtract 6−6=0 Make sure 0 < 3 R Remainder There are none left over.

The pond is 162 yards.

AP P LY Fill in the missing numbers. 1.

204

3 9 9 6 −

6 7 5 6 −

6 6 8 4 −

8 9 4 4 −

7 8 2 6 −

−

Level D

| Chapter 10 - 1

| Lighthouse MATH

Exercise | 10 - 1 Name

Divide. 1.

6 726

3 825

2 516

8 976

2 244

7 931

5 780

6 882

2 744

10. 6 684

11. 3 441

12. 8 888

14. 896 ÷ 4

15. 938 ÷ 7

16. 968 ÷ 8

13. 798 ÷ 6

Read the problem. Then solve. 17. A group of 8 friends made $968 at a bake sale. If they divide the money equally, how much will each person receive?

18. An artist has 655 glass beads for 5 art projects. If each project gets the same number of beads, how many beads will each project have?

CH AL L ENGE 19. There are 246 cupcakes. Each box holds either 2 or 3 cupcakes. If the same size boxes are used for all the cupcakes, which size would result in an even number of boxes?

Level D

| Chapter 10 - 1

| Lighthouse MATH

205

Rewrite and divide.

10 - 2 | Three-Digit Dividends with Remainders Divide. DAILY REV IE W

7 833

2 586

2 424

6 762

L E A R N A ND C ONNEC T A grocery worker has 748 cans of soup to place on 6 shelves. If the cans are put evenly on the shelves, how many cans will go on each shelf? How many will be left over? To find out how many cans go on each shelf, divide by . Divide the hundreds.

Divide the tens.

1 6 748 − 6 14

12 6 748 − 6 14 − 12 28

D Divide 6 fits into 7:

124 R4 6 748 − 6 14 − 12 28 − 24 4

D Divide 6 fits into 14:

1 time M Multiply 1×6=6 S Subtract 7−6=1 Make sure 1 < 6 B Bring down The tens digit (4) © Lighthouse Curriculum. Copying strictly prohibited.

Divide the ones.

D Divide 6 fits into 28:

2 times M Multiply 2 × 6 = 12 S Subtract 14 − 12 = 2 Make sure 2 < 6 B Bring down The ones digit (8)

4 times M Multiply 4 × 6 = 24 S Subtract 28 − 24 = 4 Make sure 4 < 6 R Remainder There are 4 left over.

There are 124 cans on each shelf with 4 cans left over.

AP P LY Fill in the missing numbers. 1.

206

6 8 3 1 −

2 2 7 1 −

5 8 9 9 −

4 5 1 8 −

−

Level D

| Chapter 10 - 2

| Lighthouse MATH

Exercise | 10 - 2 Name

Divide. 1.

5 648

6 819

3 438

6 955

2 599

2 767

3 375

4 536

5 637

10. 7 896

11. 7 852

12. 2 685

14. 858 ÷ 7

15. 946 ÷ 8

16. 928 ÷ 8

13. 737 ÷ 6

Read the problem. Then solve. 17. Tom uses 671 bricks to build a wall. If there are 5 sections of the wall, how many bricks can go in each section, and how many bricks will be left over?

18. A science class is studying 675 ants. They put the ants into containers with 6 ants in each one. How many full containers can they make? How many ants will be left over?

CH AL L ENGE 19. How can you check the answer of 514 ÷ 3 = 171 R1?

Level D

| Chapter 10 - 2

| Lighthouse MATH

207

Rewrite and divide.

10 - 3 | Zeros in Quotients Divide. DAILY REV IE W

5 584

6 673

9 183

3 245

L E A R N A ND C ONNEC T At a race, the cars go around the track 4 times. By the end of the race, they have traveled 424 feet. How many feet do they travel each time around the track? To find the number of feet each time around, divide by . Divide the hundreds.

Divide the tens.

Divide the ones.

1 4 424 − 4 02

10 4 424 − 4 2 − 0 24

106 4 424 − 4 02 − 0 24 − 24 0

D Divide 4 fits into 4:

D Divide 2 < 4, so

1 time M Multiply 1×4=4 S Subtract 4−4=0 Make sure 0 < 4 B Bring down The tens digit (2)

D Divide 4 fits into 24:

write a 0. M Multiply 0×4=0 S Subtract 2−0=2 Make sure 2 < 4 B Bring down The ones digit (4)

6 times 6 × 4 = 24 S Subtract 24 − 24 = 0 Make sure 0 < 4 R Remainder There are none left over. M Multiply

They travel 106 feet each time around.

AP P LY Fill in the missing numbers. 1.

208

6 6 1 8 −

8 8 4 0 −

9 9 2 2 −

4 5 6 0 −

−

Level D

| Chapter 10 - 3

| Lighthouse MATH

Exercise | 10 - 3 Name

Divide. 1.

9 982

7 770

4 481

6 955

9 906

9 975

3 917

4 536

2 616

10. 2 360

11. 8 966

12. 9 946

14. 916 ÷ 9

15. 782 ÷ 6

16. 760 ÷ 5

13. 968 ÷ 9

Rewrite and divide.

Read the problem. Then solve. 17. A factory makes 502 toy cars. The cars are put in boxes, with 5 cars per box. How many full boxes can the factory pack, and how many cars will be left over?

18. A gardener has 321 seeds to plant in pots. If each pot gets 3 seeds, how many pots can the gardener fill?

CH AL L ENGE 19. What is 300 ÷ 2?

Level D

| Chapter 10 - 3

| Lighthouse MATH

209

10 - 4 | Three-Digit Dividends with Two-Digit Quotients Divide. DAILY REV IE W

6 672

7 871

8 929

2 292

L E A R N A ND C ONNEC T Sarah has a book with 384 pages. She wants to read the same number of pages each day for 6 days. How many pages will she need to read each day to finish the book? To find the number of pages a day, divide

Divide the hundreds.

Divide the tens.

Divide the ones.

You can put an x above the place where you cannot divide.

6 6 384 − 36 24

64 6 384 − 36 24 − 24 0

x 6 384 D Divide 6 fits into 38:

6 times M Multiply 6 × 6 = 36 S Subtract 38 − 36 = 2 Make sure 2 < 6 B Bring down The ones digit (4)

6 does not fit into 3. 6 does fit into 38.

D Divide 6 fits into 24:

4 times M Multiply 4 × 6 = 24 S Subtract 24 − 24 = 0 Make sure 0 < 6 R Remainder There are none left over.

Sarah needs to read 64 pages a day.

AP P LY Fill in the missing numbers. 1.

9 5 0 5 − −

210

7 6 8 3 −

−

Level D

5 2 2 0 − −

| Chapter 10 - 4

| Lighthouse MATH

4 2 8 9 − −

Exercise | 10 - 4 Name

Divide. 1.

5 133

3 252

8 488

8 338

7 150

5 72

9 894

8 752

3 228

10. 5 155

11. 6 505

12. 3 215

14. 162 ÷ 9

15. 119 ÷ 2

16. 516 ÷ 9

13. 190 ÷ 3

Read the problem. Then solve. 17. A farmer has 294 eggs to pack into cartons. Each carton can hold 6 eggs. How many cartons will the farmer need?

18. A school teacher has 153 balls to divide equally among 9 classes. How many balls can each class receive?

CH AL L ENGE 19. What is 594 ÷ 10?

Level D

| Chapter 10 - 4

| Lighthouse MATH

211

Rewrite and divide.

10 - 5 | Dividing with Money Divide. DAILY REV IE W

9 531

5 245

8 792

5 211

L E A R N A ND C ONNEC T Max bought 4 flowers to plant. He spent $2.08 in total. How much was each flower? To find the amount per flower, we divide Divide the ones.

Move to the right and continue following the steps of long division. $0.5 4 $2.08 − 2 0 08

Move the dollar sign and decimal up.

$0. 4 $2.08 Since 4 does not fit into 2, write a 0. Then, divide 20 by 4.

$0.52 4 $2.08 − 2 0 8 − 8 0

D Divide

4 fits into 20: 5 times

D Divide

4 fits into 8: 2 times

M Multiply

5 × 4 = 20

M Multiply

2×4=8

S Subtract

20 − 20 = 0 Make sure 0 < 4

S Subtract

8−8=0 Make sure 0 < 4

R Remainder There are none

B Bring down The hundredths

digit (8)

left over.

Each flower cost $0.52.

AP P LY Fill in the missing numbers. 1.

$ 0 3 $ 1 5 9 − −

212

$ 0 4 $ 1 9 6 − −

Level D

| Chapter 10 - 5

$ 5 $ 8 9 0 −

$ 2 $ 6 4 6 −

−

| Lighthouse MATH

Exercise | 10 - 5 Name

Divide. 1.

2 $5.78

4 $1.00

4 $2.96

7 $2.66

7 $9.38

4 $6.80

3 $7.71

5 $8.75

9 $3.51

10. 6 $2.88

11. 7 $5.25

12. 5 $2.30

14. $5.16 ÷ 4

15. $4.83 ÷ 7

16. $3.24 ÷ 9

13. $2.70 ÷ 2

Rewrite and divide.

Read the problem. Then solve. 17. A pack of 4 soda bottles costs $1.44. What is the cost of one soda bottle?

18. 3 friends want to buy a gift for their teacher that costs $7.32. If they each give the same amount, how much will each student pay?

CH AL L ENGE 19. What is $65.00 ÷ 5?

Level D

| Chapter 10 - 5

| Lighthouse MATH

213

10 - 6 | Four-Digit Dividends Divide. DAILY REV IE W

9 $4.50

2 $9.98

3 $9.45

7 $6.93

L E A R N A ND C ONNEC T 4,824 pounds of cargo must be split equally into 6 boxes. How many pounds of cargo go into each box? To find the number of pounds in each box, divide by . Divide the thousands. x 6 4824

Divide the hundreds.

Divide the tens.

Divide the ones.

8 6 4824 − 48 02

80 6 4824 − 48 2 − 0 24

804 6 4824 − 48 02 − 0 24 − 24 0

D Divide 6 fits into

6 does not fit into 4. 6 does fit into 48.

48: 8 times M Multiply 8 × 6 = 48 S Subtract 48 − 48 = 0 Make sure 0 < 6

D Divide 6 fits into

2: 0 times M Multiply 0 × 6 = 0 S Subtract 2 − 0 = 2 Make sure 0 < 6

B Bring down

The tens digit (2)

The ones digit (4)

24: 4 times M Multiply 4 × 6 = 24 S Subtract 24 − 24 = 0 Make sure 0 < 6 R Remainder

There are none left over.

804 pounds of cargo go in each box.

AP P LY Fill in the missing numbers. 1.

214

9 4, 5 4 1 −

9 4, 2 4 7 −

7 9, 7 2 1 −

4 7, 3 1 7 −

−

Level D

| Chapter 10 - 6

| Lighthouse MATH

Exercise | 10 - 6 Name

Divide. 1.

7 9,382

5 6,350

8 3,105

3 7,501

2 6,676

3 6,954

4 2,256

7 1,126

Rewrite and divide. 7,184 ÷ 8

10. 6,247 ÷ 7

11. 6,166 ÷ 2

Read the problem. Then solve. 12. A family is driving 2,114 miles across the country. They plan to split the drive evenly over 7 days. How many miles will they need to drive each day?

13. A factory makes 6,745 water bottles per week. If they work 5 days a week, and they make the same number of bottles each day, how many water bottles do they make per day?

CH AL L ENGE 14. What is $85.24 ÷ 4?

Level D

| Chapter 10 - 6

| Lighthouse MATH

215

10 - 7 | Chapter Review Divide. DAILY REV IE W

7 2,616

7 1,421

4 648

5 3,490

L E T ' S REV I EW Dividing with Long Division Follow the steps of divide, multiply, subtract, bring down/remainder. Move to the right until there are no more digits to bring down. 124 R4 6 748 − 6 14 − 12 28 − 24 4

64 6 384 − 36 24 − 24 0

804 6 4824 − 48 02 − 0 24 − 24 0

Dividing Money

Move up the dollar sign and decimal point. Write a 0 if the divisor does not fit into a digit. Divide like whole numbers. $0.52 4 $2.08 − 2 0 8 − 8 0

AP P LY Fill in the missing numbers. 1.

7 6 2 4 − −

216

5 4, 1 0 5 −

6 8 4 0 −

4 9 0 6 −

−

Level D

| Chapter 10 - 7

| Lighthouse MATH

Exercise | 10 - 7 Name

Divide. 1.

8 966

2 703

6 535

3 436

7 5,467

3 4,746

7 762

5 2,483

Rewrite and divide. 9.

10. 742 ÷ 4

6,790 ÷ 5

11. 161 ÷ 7

12. $4,560 is to be shared equally among 3 schools. How much money does each school get?

Read the problem. Then solve. 13. A school bought 819 pencils to be divided equally among 9 classes. How many pencils will each class get?

CH AL L ENGE 14. Can you tell which problem will give the bigger answer? How? 7,358 ÷ 3

7,358 ÷ 9

Level D

| Chapter 10 - 7

| Lighthouse MATH

217

10 - 8 | Cumulative Review

Solve. 1.

7 − 4

11 − 4

3 × 7

7 × 9

1 + 6

3 − 2

8 − 6

6 + 7

2 + 1

10.

2 + 3

11.

10 − 8

12.

5 + 8

13.

6 − 1

14.

17 − 9

15.

5 + 5

16.

2 × 6

17.

3 + 5

18.

3 × 4

19.

9 + 5

20.

11 − 7

21.

6 + 3

22.

7 × 3

23.

6 + 8

24.

7 × 4

25.

12 − 9

26.

9 + 3

27.

6 × 5

28.

6 × 8

29.

2 × 8

30.

7 + 6

31.

13 − 8

32.

6 + 9

33.

6 × 3

34.

16 − 8

35.

5 × 1

36.

7 − 6

37. 1 1

38. 8 32

39. 8 56

40. 3 12

41. 8 8

42. 1 5

43. 7 63

44. 6 6

45. 5 45

46. 9 27

47. 9 9

48. 7 28

49. 3 6

50. 5 35

51. 7 42

52. 8 16

53. 4 12

54. 9 45

218

Level D

| Chapter 10 - 8

| Lighthouse MATH

Exercise | 10 - 8 Name

Add. 1.

688 + 572

251 + 761

326 + 371

6,056 + 4,149

6,440 + 9,331

1,825 + 5,468

537 − 101

740 − 141

10.

7,274 − 3,209

11.

8,563 − 4,649

12.

7,423 − 4,981

14.

22 × 7

15.

578 × 2

16.

756 × 7

17.

37 × 77

18.

47 × 85

Subtract. 7.

874 − 589

Multiply. 13.

52 × 6

Divide. 20. 6 35

21. 9 429

22. 4 156

23. 5 85

19. 9 43

Round to the highest place value. Estimate the sum or difference. 24.

192 + 258

27.

523 − 284

−

25.

682 + 28

28.

4,682 − 3,067

Level D

| Chapter 10 - 8

−

26.

8,316 + 4,693

29.

8,642 − 631

−

| Lighthouse MATH

219

11 C H A P T E R

220

In Chapter 11 we will learn about

Fractions Fractions are numbers that show a part of a whole or a part of a set. We use fractions in the real world when we bake and measure. • We will review what the parts of a fraction tell us about the number. • We will find equivalent fractions using pictures, multiplication, and division. • We will put fractions in their simplest form. • We will compare fractions using number lines, numerators and denominators. • We will learn about improper fractions and mixed numbers.

221

11 - 1 | Introduction to Fractions Solve. 1.

DAILY REV IE W

5,731 + 2,702

4,721 − 592

392 × 6

4 268

L E A R N A ND C ONNEC T A fraction can show parts of a whole:

A fraction can show parts of a set:

The cake was divided into 8 equal slices. There are 3 slices left.

There are 5 ducks. 2 of them are blue.

We can write the fraction of cake left.

We can write the fraction of ducks that are blue.

Slices left Equal parts

numerator

Blue ducks

denominator

All the ducks

There are three-eighths of the cake left.

numerator

denominator

Two-fifths of the ducks are blue.

AP P LY Write a fraction to show the part of chocolate bar that is left. 1.

Vocabulary Numerator - the top number in a fraction

222

Denominator - the bottom number in a fraction

Level D

| Chapter 11 - 1

| Lighthouse MATH

Exercise | 11 - 1 Name

Write the fraction that shows the part that is red. 1.

2. 4

Write the fraction that shows the part that is not red. 7.

9. 3

10.

11.

12.

Read the problems. Then solve. 13. Jack had 10 toy cars. 8 were red. What fraction of his cars were red?

14. There are 9 pens in the drawer. 3 of them are blue. What fraction of the pens are blue?

CH AL L ENGE Shade in each figure to show the fraction. 2

15. 5

16. 4

Level D

17.

| Chapter 11 - 1

3 8

| Lighthouse MATH

18. 8

223

11 - 2 | Equivalent Fractions Write the fraction to show what part of each figure is blue. 1.

DAILY REV IE W

L E A R N A ND C ONNEC T Two or more fractions can show the same amount. We call them equivalent fractions. We can use a picture to make equivalent fractions. Color the number of pieces that show the same amount. 1 2 of a cake

2 4 of a cake

1 2 4 = = 2 4 8

When we color 4 slices in the last cake, it shows the same amount as 21 and 42 . © Lighthouse Curriculum. Copying strictly prohibited.

? 8 of a cake

AP P LY Color the number of parts that show the same amount. Write the missing numerator. 1.

1 4 = 8

2 3 = 6

Vocabulary Equivalent fractions - two or more fractions that show the same amount

224

Level D

Numerator - the top number in a fraction Denominator - the bottom number in a fraction

| Chapter 11 - 2

| Lighthouse MATH

5 6 = 12

Exercise | 11 - 2 Name

Color the number of parts that show the same amount. Write the missing numerator. 2.

1 3 = 9

8 4 = 16

3 3 = 6

1 3 = 6

6 5 = 10

4 2 = 8

3 4 = 8

1 2 = 4

2 4 = 8

CH AL L ENGE Use the pictures to solve the problem. 10. Kim is allowed to eat 31 of the chocolate bar. The bar is broken into 6 equal pieces. How many pieces is Kim allowed to eat?

Level D

11. The recipe needs 21 cup of sugar, but Ann can only find the 41 measuring cup. How many 41 cups should she use?

| Chapter 11 - 2

| Lighthouse MATH

225

11 - 3 | Finding Equivalent Fractions Color the number of parts that show the same amount. Write the missing numerator. 1.

DAILY REV IE W 1 2 = 8

2 3 = 6

3 4 = 8

L E A R N A ND C ONNEC T To find an equivalent fraction, we can multiply the numerator and denominator by the same number. Whatever you do to the top, you must do to the bottom. Find fractions that are equivalent to 1 . 3 Choose a number to multiply by. Multiply the top. Multiply the bottom.

1 ×2 = 2 3 ×2 6

1 ×3 = 3 3 ×3 9

1 ×4 = 4 3 × 4 12

1 = 2 = 3 = 4 3 6 9 12

AP P LY Multiply the numerator and denominator by the same number to find an equivalent fraction. 1.

1 × 2 2 × 2=

1 × 3 2 × 3=

1 × 4 2 × 4=

1 × 5 2 × 5=

3 × 2 4 × 2=

3 × 3 4 × 3=

3 × 5 4 × 5=

3 × 10 4 × 10 =

1 × 6 10 × 6 =

10. 10 × 8 =

1 × 8

11. 10 × 10 =

1 × 10

12. 10 × 12 =

Vocabulary Equivalent fractions - two or more fractions that show the same amount

226

Level D

Numerator - the top number in a fraction Denominator - the bottom number in a fraction

| Chapter 11 - 3

| Lighthouse MATH

1 × 12

Exercise | 11 - 3 Name

Multiply the numerator and denominator by the same number to find equivalent fractions. 1.

1 × 2 2 × 2=

1 × 5 2 × 5=

2 × 4 3 × 4=

2 × 3 5 × 3=

5 × 2 6 × 2 =

4 × 2 5 × 2 =

1 × 3 6 × 3 =

3 × 4 4 × 4 =

1 × 5 3 × 5 =

10. 7 × 10 =

2 × 10

11. 8 × 2 =

3 × 2

12. 10 × 3 =

1 × 5

2 × 5

13. 4 × 5 = 20

14. 3 × 5 = 6

3 × 3

3 × 5

1 × 5

15. 4 × 5 = 12

16. 10 × 5 = 30

1 4 =

18. 5 =

19. 4 =

20. 6 =

22. 8 =

17.

21. 9 =

Find three equivalent fractions.

CH AL L ENGE Fill in the missing numbers. 1

23. 6 = 12

24. 5 = 15

Level D

| Chapter 11 - 3

25. 2 = 10

| Lighthouse MATH

26. 5 = 10

227

11 - 4 | Simplifying Fractions Write the missing numerators. 1.

DAILY REV IE W

1 × 4 2 × 4= 8

5 × 2 6 × 2 = 12

2 × 3 3 × 3= 9

L E A R N A ND C ONNEC T We can also find an equivalent fraction by dividing the numerator and denominator by the same number. When we divide, the top and bottom numbers get smaller. This is called simplifying. Whatever you do to the top, you must do to the bottom.

Finishing 4 out of 8 questions is the 1 same as finishing of the the test. 2

Simplify 4 8 Find a number that the numerator and denominator can both be divided by.

Divide the top. Divide the bottom.

Solve.

4 and 8 can both be divided by 4 or 2.

4 ÷4 = 1 8 ÷4 2

4 = 1 8 2

AP P LY Divide the numerator and denominator by the same number to simplify the fraction. 1.

3 ÷ 3 9 ÷ 3=

2 ÷ 2 4 ÷ 2=

4 ÷ 2 6 ÷ 2=

10 ÷ 5 15 ÷ 5 =

12 ÷ 2 24 ÷ 2 =

6 ÷ 2 12 ÷ 2 =

3 ÷ 3 6 ÷ 3=

8 ÷ 4 32 ÷ 4 =

Vocabulary Simplifying a fraction - dividing the numerator and denominator by the same number to make an equivalent fraction with smaller numbers Equivalent fractions - two or more fractions that show the same amount Numerator - the top number in a fraction Denominator - the bottom number in a fraction

228

Level D

| Chapter 11 - 4

| Lighthouse MATH

Exercise | 11 - 4 Name

Divide the numerator and denominator by the same number to simplify the fraction. 1.

4 ÷ 2 10 ÷ 2 =

6 ÷ 3 9 ÷ 3=

5 ÷ 5 25 ÷ 5 =

14 ÷ 2 16 ÷ 2 =

12 ÷ 6 18 ÷ 6 =

4 ÷ 4 16 ÷ 4 =

18 ÷ 6 24 ÷ 6 =

21 ÷ 7 28 ÷ 7 =

10 ÷ 10 30 ÷ 10 =

10. 20 ÷ 5 =

15 ÷ 5

11. 24 ÷ 8 =

8 ÷ 8

12. 27 ÷ 9 =

6 ÷ 3

14. 21 ÷ 3 =

9 ÷ 3

15. 16 ÷ 3 =

8 ÷ 3

16. 35 ÷ 3 =

12 ÷ 3

18. 30 ÷

18 ÷

19. 20 ÷ 3 =

14 ÷ 3

20. 24 ÷ 3 =

12 ÷ 3

22. 45 ÷ 3 =

23. 36 ÷ 3 =

16 ÷ 3

24. 8 ÷ 3 =

17. 28 ÷ 3 =

21. 15 ÷ 3 =

30 ÷

25. 50 ÷

25 ÷ 3

16 ÷

26. 40 ÷

10 ÷

27. 16 ÷

15 ÷ 3

20 ÷ 3

2 ÷ 3

36 ÷

28. 42 ÷

13. 8 ÷ 3 =

9 ÷ 9

CH AL L ENGE A fraction is in simplest form when it can’t be simplified anymore. Write each fraction in simplest form. 16

29. 28 =

30. 54 =

Level D

31. 56 =

| Chapter 11 - 4

| Lighthouse MATH

32. 48 =

229

11 - 5 | Comparing Fractions on a Number Line Divide by a fraction equal to 1 to simplify the fraction. 1.

DAILY REV IE W

6 ÷ 4 10 ÷ 4 =

6 ÷ 6 12 ÷ 6 =

4 ÷ 2 18 ÷ 2 =

L E A R N A ND C ONNEC T We can see fractions on a number line. Fractions that are closer to 1 are bigger than fractions closer to 0.

0 2

1 2

2 2

1 3

2 3

0 3

1 3

1 4

3 3

0 4 0

2 3

2 4

3 4

1 4

2 4

3 4

4 4

0 5

2 3 is smaller than . 3 4

1 5

2 5

3 5

4 5

5 5

0 1 10 10

2 10

3 10

4 10

5 10

6 10

7 10

8 10

9 10

10 10

AP P LY Shade the number line to show the fraction. 1. 3.

2 3

6 10

1 3

2 3

0 1 2 3 4 5 6 7 8 9 10 10 10 10 10 10 10 10 10

4. 1

1 2

4 5

1 5

2 5

3 5

4 5

Draw a dot to show where the fraction is on the number line. 5.

5 7

1 4

3 6

2 9

Vocabulary Equivalent fractions - two or more fractions that show the same amount

230

Level D

Numerator - the top number in a fraction Denominator - the bottom number in a fraction

| Chapter 11 - 5

| Lighthouse MATH

Exercise | 11 - 5 Name

Write < for less than or > for greater than. 1.

1 2

1 1

3 8

1 2

5 6

1 3

5 8 1

1 4

4 5

2 5

2 3

1 6

1 4

3 4

3 10

1 3

4 5

10. 0

2 5

1 2 1 1

2 3

3 5

11. A recipe calls for 43 of a cup of sugar. You only have 32 of a cup. Is 32 of a cup more or less sugar than 43 of a cup?

12. Lisa practiced the piano for 65 of an hour. Anna practiced for 43 of an hour. Who practiced for longer?

CH AL L ENGE Compare the fractions. Explain how you know which is bigger. 158

13. 159

157 158

Level D

| Chapter 11 - 5

| Lighthouse MATH

231

Read the problem. Then solve.

11 - 6 | Comparing Fractions Write < for less than or > for greater than. 1.

DAILY REV IE W

3 5

4 5

7 10

3 4

L E A R N A ND C ONNEC T When fractions have the same denominator, we can compare the numerators. A bigger numerator means a bigger fraction.

> 3 4

If two fractions have different denominators, we can write new equivalent fractions with the same denominator and then compare them.

2 3

3 4

3 is greater than 1 4 4

1 4

2 × 4= 8 3 × 4 12

3 × 3= 9 4 × 3 12

2 is less than 3 3 4

AP P LY Write < for less than or > for greater than. 1.

7 8

5 8

3 6

5 6

2 5

1 5

1 6

4 6

1 8

4 8

4 5

1 5

2 3

1 3

4 7

3 7

3 9

1 9

10. 7

4 7

11. 6

1 6

12. 7

5 7

5 6

14. 9

4 9

15. 9

5 9

16. 9

4 9

13. 6 Vocabulary

Equivalent fractions - two or more fractions that show the same amount

232

Level D

Numerator - the top number in a fraction Denominator - the bottom number in a fraction

| Chapter 11 - 6

| Lighthouse MATH

Exercise | 11 - 6 Name

Find equivalent fractions that have the same denominator. Then, write < for less than or > for greater than. 2 3

1 ×3 2 ×3 =

2 ×2 3 ×2 =

3 5

5 8

2 6

3 6

1 4

3 ×2 6 ×2 =

2 5

2 ×5 6 ×5 =

6 7 6 ×3 7 ×3 =

6. 1 ×8 2 ×8 =

2 3 2 ×7 3 ×7 =

1 2

5 ×2 8 ×2 =

1 ×3 4 ×3 =

4. 3 ×5 4 ×5 =

1 4

1 ×4 3 ×4 =

3 4

3 ×4 5 ×4 =

1 3

1 ×3 4 ×3 =

3 8

8. 2 ×6 5 ×6 =

1 3

3 ×3 8 ×3 =

1 ×8 3 ×8 =

CH AL L ENGE 1 3

9. 1 × 3 ×

1 4

3 7 3 × 7 ×

= 14

2 5

12. 2 × 6 ×

Level D

1 × 2 ×

= 12

2 6

1 2

10. 3 × 4 ×

= 12

11. 1 × 4 ×

3 4

2 × 5 ×

| Chapter 11 - 6

| Lighthouse MATH

= 14

1 4 1 × 5 4 × 5 =

233

1 2

11 - 7 | Improper Fractions Write > for greater than. Write < for less than. DAILY REV IE W

2 3

3 5

1 4

3 8

5 6

4 5

7 10

3 4

L E A R N A ND C ONNEC T When the numerator of a fraction is bigger than the denominator, it is called an improper fraction. Improper fractions are greater than 1. Each slice is 1 of the pizza. 8 There are 20 slices. There are 20 of pizza. 8

AP P LY Write an improper fraction for each picture.

2. 4

4. 8

6. 5

Vocabulary Improper fraction - a fraction where the numerator is greater than the denominator; a fraction greater than one

234

Level D

Numerator - the top number in a fraction Denominator - the bottom number in a fraction

| Chapter 11 - 7

| Lighthouse MATH

Exercise | 11 - 7 Name

Write an improper fraction for each picture. 1.

Draw a picture to show each improper fraction. 7 3

8 5

9 2

5 4

10 6

10. 7

CH AL L ENGE 11. A bakery cuts its cakes into fourths and sells them by the slice. If you want 2 whole cakes and 1 extra slice, what fraction of cake do you need to buy?

Level D

| Chapter 11 - 7

| Lighthouse MATH

235

11 - 8 | Mixed Numbers Draw a picture to show each improper fraction. DAILY REV IE W

6 4

21 9

L E A R N A ND C ONNEC T Improper fractions can be written as mixed numbers. A mixed number tells the number of wholes, and the extra is written as a fraction part.

There are 2 whole cookies. 2 There is an extra of a cookie. 3 2 There are 2 cookies. 3 We can write the number of cookies in two ways:

Improper fraction: 8 3

Mixed number: 2 2 3

AP P LY Write a mixed number for each picture. 1.

Vocabulary Mixed number - a whole number with an extra fraction part Improper fraction - a fraction where the numerator is greater than the denominator; a fraction greater than one Numerator - the top number in a fraction Denominator - the bottom number in a fraction

236

Level D

| Chapter 11 - 8

| Lighthouse MATH

Exercise | 11 - 8 Name

Draw a picture of the improper fraction. Write the equivalent mixed number. Improper fraction

7 4

11 6

32 10

14 3

Drawing

Mixed number

Draw a picture of the mixed number. Write the equivalent improper fraction. Mixed number

Drawing

Improper fraction

CH AL L ENGE 9. Sara is putting away blocks on the shelves. She has 20 blocks, and each shelf holds 6 blocks. How many shelves will she fill? Write the answer as a mixed number.

Level D

| Chapter 11 - 8

| Lighthouse MATH

237

11 - 9 | Comparing Mixed Numbers Draw a picture to show each mixed number. DAILY REV IE W

L E A R N A ND C ONNEC T We can see mixed numbers on a number line. A mixed number will be between two whole numbers. To see which mixed number is bigger, check which is closer to the largest whole number.

1 3

1 4

2 3

2 4

3 4

11 3

11 4

12 3

12 4

13 4

21 3

21 4

22 3

22 4

23 4

To compare fractions without a number line: If the whole numbers are the same, compare the fractions.

First, compare the whole numbers.

22 3

1 ? 24

1 > 2 4

AP P LY Write < for less than or > for greater than. 1.

21 4

22 4

23 4

21 3

22 3

41 3

42 3

41 5

42 5

43 5

44 5

11 5

13 5

31 4

32 4

Vocabulary

238

Level D

| Chapter 11 - 9

Numerator - the top number in a fraction Denominator - the bottom number in a fraction

| Lighthouse MATH

33 4

3 3 1 32 33 34 35 36 37 8 8 8 8 8 8 8

Equivalent fractions - two or more fractions that show the same amount Mixed number - a whole number with an extra fraction part

14 5

11 2

12 5

Exercise | 11 - 9 Name

Write < for less than or > for greater than. 1.

61 5

62 5

63 5

64 5

6 6 1 62 63 64 65 66 67 8 8 8 8 8 8 8

11 4

11 6

12 4 12 6

13 6

13 4 14 6

71 5

73 5

74 5

7 1 72 73 74 75 76 77 8 8 8 8 8 8 8

21 4

15 6

72 5

21 6

22 4 22 6

23 6

23 4 24 6

81 5

31 4

31 6

32 6

33 6

10. 1 4

12. 6 9

1 9

13. 5 3

14. 2

84 5

32 4

11. 3 2

83 5

8 8 1 82 83 84 85 86 87 8 8 8 8 8 8 8

25 6

82 5

33 4 34 6

7 9

35 6

7 8

15. The Blue Trail is 5 31 miles long. The Red Trail is 5 61 miles long. Which trail is longer?

Read the problem. Then solve. 16. During field day, Barry jumped 3 25 meters. Marcus jumped 3 45 meters. Who jumped a longer distance?

CH AL L ENGE Compare the mixed numbers and improper fractions. Write < for less than or > for greater than. 3

17. 1 6

7 4

18. 2 5

Level D

2 10

| Chapter 11 - 9

19. 3

| Lighthouse MATH

20. 5

45 8

239

11 - 10 | Chapter Review Write < for less than or > for greater than. DAILY REV IE W

7 8

8 9

L E T ' S REV I EW Writing Fractions

Equivalent Fractions

1 = 2 4 8 3 of the circles are red. 5

1 ×2 2 = 4 ×2 8

Improper Fractions and Mixed Numbers

Comparing Fractions and Mixed Numbers 11 2

3 4

11 3 or 2 of the circles are green. 4 4

1 2

0 0

2 ÷2 1 = 8 ÷2 4

1 4

2 4

11 2

1 3 4

11 4

12 4

2 13 4

Compare the whole numbers. Compare the fractions.

AP P LY Write the fraction, improper fraction, or mixed number that shows the part that is red. 1.

Fraction:

240

Fraction:

Level D

| Chapter 11 - 10

Improper Fraction:

| Lighthouse MATH

Mixed number:

Exercise | 11 - 10 Name

Color the number of parts that show the same amount. Write the missing numerator. 1.

1 4 = 8

2 3 = 9

1 2 = 8

Write the missing numbers. 4.

1 × 2 6 × 2=

4 × 3 5 × 3=

3 × 2 4 × 2=

2 × 3 × 4 =

8 × 3 = 9 ×

10. 6 ×

1 ×

= 18

1 × 3 2 × 3=

4 ×

11. 7 ×

= 14

Divide by a fraction equal to 1 to simplify the fraction. 13. 15 ÷ 3 =

8 ÷ 4

17. 21 ÷ 3 =

16. 20 ÷ 4 =

6 ÷ 3

14. 30 ÷ 5 =

25 ÷ 5

15. 18 ÷ 2 =

16 ÷ 2

9 ÷ 3

18. 100 ÷ 10 =

70 ÷ 10

19. 10 ÷ 2 =

23. 4

2 ÷ 2

12. 8 ÷ 2 =

6 ÷ 2

Write < for less than or > for greater than. 1

3 6

20. 6

24. 5 4

2 3

21. 2

25. 3 4

Level D

1 6

22. 6

3 4

| Chapter 11 - 10

26. 6 2

| Lighthouse MATH

27. 1

1 8

4 5

241

11 - 11 | Cumulative Review

Solve. 1.

5 + 4

8 × 9

12 − 6

6 + 6

2 + 7

2 × 5

5 − 1

8 − 3

5 + 9

10.

9 + 5

11.

5 + 7

12.

4 × 3

13.

9 × 5

14.

2 + 1

15.

10 − 7

16.

10 − 9

17.

11 − 2

18.

3 − 2

19.

4 + 4

20.

8 × 1

21.

3 + 4

22.

8 + 5

23.

1 × 7

24.

9 × 3

25.

13 − 7

26.

5 + 3

27.

7 + 9

28.

7 × 2

29.

12 − 3

30.

6 − 2

31.

7 + 4

32.

6 + 4

33.

7 − 6

34.

10 − 6

35.

4 + 9

36.

8 × 6

37. 3 3

38. 7 28

39. 5 40

40. 7 42

41. 7 7

42. 9 45

43. 1 5

44. 4 16

45. 8 48

46. 2 16

47. 5 45

48. 2 10

49. 3 9

50. 5 15

51. 7 28

52. 8 24

53. 4 20

54. 6 54

242

Level D

| Chapter 11 - 11

| Lighthouse MATH

Exercise | 11 - 11 Name

Add. 1.

4,487 + 1,931

7,328 + 6,014

2,407 + 7,372

7,198 + 4,865

5,432 + 9,835

7,527 − 4,917

4,064 − 2,694

7,552 − 416

10.

6,614 − 548

Subtract. 6.

4,609 − 2,330

Multiply. 11.

96 × 4

12.

34 × 1

13.

47 × 4

14.

52 × 7

15.

72 × 31

16.

61 × 52

Divide. 18. 3 164

19. 6 342

20. 2 1,704

21. 8 936

17. 8 559

Write the amount of money. 22.

23.

Level D

| Chapter 11 - 11

| Lighthouse MATH

243

12 C H A P T E R

244

In Chapter 12 we will learn about

Operations with Fractions Fractions can be combined, separated, added, and subtracted. In this chapter, we will use pictures to understand what happens when fractions are joined or taken away. Then we will learn how to add and subtract fractions and mixed numbers with the same denominator. • We will combine fractions using pictures. • We will remove fractions using pictures. • We will add and subtract fractions that have the same denominator. • We add and subtract mixed numbers that have the same denominator.

245

12 - 1 | The Unit Fraction Solve. 1.

DAILY REV IE W

12 × 2

10 × 6

26 × 5

18 × 3

14 × 4

19 × 2

L E A R N A ND C ONNEC T A unit fraction has a numerator of 1. It shows one equal part of a whole. Every fraction is made up of unit fractions. The whole is made up of 6 equal pieces. 1 Each piece is . 6 3 pieces are shaded.

1 6

1 1 1 3 + + = 6 6 6 6 3 of the whole is shaded. 6

1 6

Whole =

6 6

1 6

3 6

AP P LY Write each unit fraction. 1.

Vocabulary Unit fraction - a fraction that represents one part of a whole; it has a numerator of 1 Numerator - the top number in a fraction that shows the part of the whole Denominator - the bottom number in a fraction that shows number of equal parts in the whole

246

Level D

| Chapter 12 - 1

| Lighthouse MATH

1 6

Exercise | 12 - 1 Name

Solve. 1.

Color in 4 pieces. What size is each piece?

Color in 2 pieces. What size is each piece?

1 1 1 1 10 + 10 + 10 + 10 =

1 1 1 1 8 + 8 + 8 + 8 =

1 1 6 + 6 =

Answer the question. Then fill in the number sentence. 4.

How many 4 size pieces are there?

How many 3 size pieces are there?

How many 5 size pieces are there?

1 4 +

1 3 +

1 5 +

How many 8 size pieces are there?

How many 6 size pieces are there?

1 8 +

1 6 +

CH AL L ENGE Solve. 1

9. How many 4 size pieces are there? 1 4 +

Level D

| Chapter 12 - 1

| Lighthouse MATH

247

12 - 2 | Combining Fractions Write the fraction. 1.

DAILY REV IE W

L E A R N A ND C ONNEC T We can use a picture to add fractions. 1

Ron eats 5 of a cake. His family eats 5 of the cake. What fraction of the cake did they eat in all? To find the fraction of cake they ate, add Shade

1 . 5

1 5

and Shade

1 5

. 3 . 5

1 5

Count the number of shaded pieces. There are 4 shaded pieces. 1 1 1 1 1 4 + + + += Each piece is . 5 5 5 5 5 5 4

They ate 5 of the cake in all.

AP P LY Shade. Then add. 1.

2. 1

Shade 6 . 3 Shade another 6 .

1 3 6 + 6 =

2 3 8 + 8 =

4. 1

Shade 5 . 1 Shade another 5 .

248

Shade 8 . 3 Shade another 8 .

1 1 5 + 5 =

Level D

| Chapter 12 - 2

Shade 7 . 2 Shade another 7 .

| Lighthouse MATH

4 2 7 + 7 =

Exercise | 12 - 2 Name

Shade. Then add. 2.

Shade 10 . 3 Shade another 10 .

Shade 7 . 3 Shade another 7 .

Shade 10 . 5 Shade another 10 .

2 3 10 + 10 =

4 3 7 + 7 =

3 5 10 + 10 =

Shade 4 . 1 Shade another 4 .

Shade 8 . 5 Shade another 8 .

Shade 6 . 1 Shade another 6 .

2 1 4 + 4 =

2 5 8 + 8 =

2 1 6 + 6 =

Shade 9 . 4 Shade another 9 .

Shade 6 . 2 Shade another 6 .

Shade 5 . 2 Shade another 5 .

3 4 9 + 9 =

2 2 6 + 6 =

2 2 5 + 5 =

10.

11.

12.

Shade 12 . 6 Shade another 12 .

Shade 8 . 3 Shade another 8 .

Shade 5 . Shade another 1 2 5 . Shade another 5 .

5 6 12 + 12 =

1 3 8 + 8 =

2 5 +

CH AL L ENGE Solve. 5

13. George has read 12 of the pages in his book. 2 He will read 12 more soon. What fraction of George’s book will he have left?

Level D

| Chapter 12 - 2

| Lighthouse MATH

249

12 - 3 | Removing Fractions Shade the fractions to add. 1.

DAILY REV IE W

2. 1 3 6 + 6 =

3. 2 3 10 + 10 =

1 3 8 + 8 =

L E A R N A ND C ONNEC T We can use pictures to subtract fractions. 7

Hannah has 12 of a package of eggs. 4 Her recipe uses 12 of a package. What fraction of the package will be left? To find the fraction left, subtract

1 12

from

1 12

7 4 3 − = 12 12 12 7

There is 12 of the package left.

AP P LY Shade. Then cross out to subtract. 1.

2. 5

Shade 6 . 3 Cross out 6 .

5 3 6 − 6 =

6 5 7 − 7 =

4. 7

Shade 8 . 3 Cross out 8 . 250

Shade 7 . 5 Cross out 7 .

7 3 8 − 8 =

Level D

| Chapter 12 - 3

Shade 8 . 5 Cross out 8 . | Lighthouse MATH

6 5 8 − 8 =

Exercise | 12 - 3 Name

Shade. Then subtract. 2.

Shade 12 . 5 Cross out 12 .

Shade 11 . 4 Cross out 11 .

Shade 10 . 7 Cross out 10 .

11 5 12 − 12 =

10 4 11 − 11 =

8 7 10 − 10 =

Shade 8 . 5 Cross out 8 .

Shade 7 . 1 Cross out 7 .

Shade 12 . 5 Cross out 12 .

7 5 8 − 8 =

5 1 7 − 7 =

9 5 12 − 12 =

Shade 11 . 3 Cross out 11 .

Shade 6 . 2 Cross out 6 .

Shade 8 . 2 Cross out 8 .

10 3 11 − 11 =

4 2 6 − 6 =

5 2 8 − 8 =

10.

11. 5

12. 3

Shade 6 . 1 Cross out 6 .

Shade 4 . 2 Cross out 4 .

Shade 12 . 8 Cross out 12 .

5 1 6 − 6 =

3 2 4 − 4 =

11 8 12 − 12 =

CH AL L ENGE Read the problem. Then solve. 5

13. Max has 1 8 chocolate 7 bars. He eats 8 of a bar. How much does he have left?

Level D

| Chapter 12 - 3

| Lighthouse MATH

251

12 - 4 | Adding and Subtracting Fractions Shade and cross out to subtract. 1.

DAILY REV IE W

2. 7 4 8 − 8 =

3. 3 1 4 − 4 =

4 2 5 − 5 =

L E A R N A ND C ONNEC T When the denominators are the same, we can add or subtract the numerators and keep the denominator. Adding Fractions

Subtracting Fractions

Add the numerators.

Keep the denominator.

Subtract the numerators.

Keep the denominator.

1 4 5 + = 6 6

1 4 5 + = 6 6 6

6 1 5 − = 8 8

6 1 5 − = 8 8 8

AP P LY

Add. 1.

1 2 4 + 4 = 4

2 2 5 + 5 = 5

1 5 8 + 8 = 8

5 3 12 + 12 = 12

2 3 6 + 6 =

2 3 7 + 7 =

2 7 10 + 10 =

4 6 11 + 11 =

11. 6 − 6 = 6

12. 11 − 11 = 11

15. 12 − 12 =

16. 10 − 10 =

Subtract. 9.

5 2 8 − 8 = 8

10. 5 − 5 = 5

14. 4 − 4 =

13. 7 − 7 =

252

Level D

| Chapter 12 - 4

| Lighthouse MATH

Exercise | 12 - 4 Name

Add. 1.

3 5 12 + 12 =

6 8 15 + 15 =

5 3 11 + 11 =

11 22 40 + 40 =

37 12 50 + 50 =

2 3 8 + 8 =

13 6 20 + 20 =

3 9 14 + 14 =

6 2 9 + 9 =

10. 16 + 16 =

11. 16 + 16 =

12. 7 + 7 =

14. 8 + 8 =

15. 12 + 12 =

16. 4 + 4 =

13. 10 + 10 =

4 2 7 − 7 =

18. 8 − 8 =

19. 12 − 12 =

20. 15 − 15 =

21. 16 − 16 =

22. 11 − 11 =

23. 6 − 6 =

24. 15 − 15 =

25. 10 − 10 =

26. 15 − 15 =

27. 7 − 7 =

28. 7 − 7 =

30. 19 − 19 =

31. 20 − 20 =

32. 18 − 18 =

17.

29. 9 − 9 =

Subtract.

CH AL L ENGE Tell whether the number sentence is true or false. Explain. 5

33. 8 + 8 = 16

Level D

| Chapter 12 - 4

| Lighthouse MATH

253

12 - 5 | Adding and Subtracting Mixed Numbers Solve. 1.

DAILY REV IE W

1 2 5 + 5 =

1 1 4 + 4 =

4 1 7 + 7 =

1 3 6 + 6 =

L E A R N A ND C ONNEC T When we add or subtract mixed numbers with the same denominator, we solve one part at a time.

Adding Mixed Numbers Add the whole numbers.

Add the fractions. 2

2 1 +1 = 5 5

Subtracting Mixed Numbers

3 5

Subtract the whole numbers.

Subtract the fractions.

2 1 3 +1 =3 5 5 5

3 2 −1 = 4 4

1 4

3 2 1 −1 =1 4 4 4

AP P LY

Solve. 1

2 5 +2 5 =

23 +33 =

38 −18 =

14 +14 =

1 5 +1 5 =

48 −18 =

254

Level D

18 +18 =

14 +34 =

2 7 −1 7 =

| Chapter 12 - 5

| Lighthouse MATH

Exercise | 12 - 5 Name

Add. 1

14 +14 =

1 5 +1 5 =

74 +24 =

13. 4 5 − 1 5 =

16. 3 5 − 1 5 =

19. 5 3 − 3 3 =

23. 8 9 − 2 9 =

63 +23 =

29 +29 =

14 +14 =

10. 2 3 + 3 3 =

38 +18 =

23 +33 =

68 +28 =

11. 5 12 + 3 12 =

12. 2 3 + 3 3 =

14. 8 4 − 2 4 =

15. 3 7 − 1 7 =

17. 6 8 − 1 8 =

18. 2 4 − 1 4 =

20. 3 4 − 1 4 =

21. 2 10 − 1 10 =

24. 3 6 − 3 6 =

22. 5 10 − 2 10 =

Subtract.

CH AL L ENGE Add. 3

25. 24 +14 =

26. 9 8 + 3 8 =

Level D

| Chapter 12 - 5

27. 11 3 + 2 3 =

| Lighthouse MATH

255

12 - 6 | Chapter Review Identify the unit fraction. 1.

DAILY REV IE W

L E T ' S REV I EW Unit Fractions

Adding and Subtracting Fractions with a Picture To add, shade both numbers. To subtract, shade the first number, then cross out the second number.

Each piece is

1 . 8

1 5

6 pieces are shaded.

1 5

1 2 3 + = 5 5 5

1 1 1 1 1 1 6 + + + + + = 8 8 8 8 8 8 8

1 5 4 3 1 − = 6 6 6

Adding and Subtracting Fractions

Adding and Subtracting Mixed Numbers

Add or subtract the numerators. Keep the denominator the same.

Add or subtract the fractions. Add or subtract the wholes.

3 1 4 + = 8 8 8

3 1 2 − = 8 8 8

1 3 +3 5 5 1 3 4 + = 2+3=5 5 5 5 4 5 5

5 4 −3 9 9 5 4 1 − = 5−3=2 9 9 9 1 2 9

AP P LY Write a fraction to show the part that is blue. 1.

256

How many 6 size pieces are there?

How many 3 size pieces are there?

How many 5 size pieces are there?

1 6 +

1 1 3 + 3 =

1 5 +

Level D

| Chapter 12 - 6

| Lighthouse MATH

Exercise | 12 - 6 Name

Shade. Then add. 2.

Shade 10 . 3 Shade another 10 .

Shade 5 . 3 Shade another 5 .

Shade 9 . 2 Shade another 9 .

4 3 10 + 10 =

1 3 5 + 5 =

2 2 9 + 9 =

Shade. Then subtract. 4.

Shade 12 . 4 Cross out 12 .

Shade 9 . 6 Cross out 9 .

Shade 4 . 1 Cross out 4 .

10 4 12 − 12 =

7 6 9 − 9 =

3 1 4 − 4 =

3 2 11 + 11 =

11. 10 − 10 =

15. 9 5 − 5 5 =

20. 2 4 + 4 4 =

19. 9 12 − 4 12 =

5 2 9 − 9 =

12. 12 + 12 =

16. 3 3 + 2 3 =

21. 9 11 + 1 11 =

Level D

| Chapter 12 - 6

7 1 10 + 10 =

10. 8 − 8 =

13. 8 − 8 =

14. 16 + 16 =

17. 9 4 + 3 4 =

18. 5 10 + 3 10 =

22. 4 5 + 1 5 =

| Lighthouse MATH

Solve.

257

12 - 7 | Cumulative Review

Solve. 1.

15 − 7

7 + 9

13 − 8

1 × 6

3 × 4

1 + 9

7 × 4

2 + 4

2 × 9

10.

6 + 6

11.

4 + 9

12.

4 × 3

13.

2 + 8

14.

6 − 1

15.

3 × 3

16.

2 × 7

17.

14 − 9

18.

10 − 5

19.

5 + 8

20.

3 × 1

21.

9 + 4

22.

1 + 8

23.

10 − 2

24.

4 + 3

25.

7 − 4

26.

4 × 5

27.

4 + 7

28.

2 × 8

29.

8 − 2

30.

6 − 5

31.

6 + 5

32.

9 − 8

33.

4 × 6

34.

7 + 3

35.

5 + 3

36.

2 × 3

37. 1 9

38. 3 15

39. 1 4

40. 8 24

41. 9 45

42. 1 5

43. 7 42

44. 2 2

45. 4 8

46. 1 7

47. 2 8

48. 8 32

49. 5 35

50. 7 35

51. 9 81

52. 9 72

53. 6 48

54. 6 42

258

Level D

| Chapter 12 - 7

| Lighthouse MATH

Exercise | 12 - 7 Name

Add. 1.

257 + 278

728 + 977

403 + 204

1,367 + 7,313

9,304 + 3,900

802 − 10

409 − 204

8,497 − 555

10.

5,051 − 3,270

Subtract. 6.

341 − 52

Multiply. 11.

356 × 4

12.

761 × 3

13.

14.

8,431 × 7

3,687 × 4

15.

49 × 77

16.

58 × 28

Divide. 18. 6 447

19. 6 4,755

20. 2 1,714

Compare. Write < or > on the line. 21. 639 24. 32,546

693

332,432

22. 480

408

25. 30,002

30,004

23. 3,942 26. 3,468,382

3,432

4,732,354

Write the numbers in order from least to greatest. 27. 4,324; 3,623; 7,298

28. 97,435; 83,335; 97,452

Level D

| Chapter 12 - 7

29. 385,932; 254,365; 254,065

| Lighthouse MATH

259

17. 2 129

13 C H A P T E R

260

In Chapter 13 we will learn about

Decimals Fractions can also be written using place value. We call these numbers decimals because we put a decimal point between the wholes and parts. • We will write a fraction with a denominator of 10 as a number with one decimal place. • We will write a fraction with a denominator of 100 as a number with two decimal places. • We will write decimals with whole numbers. • We will compare and order decimals.

261

13 - 1 | Tenths Add. 1.

DAILY REV IE W

1 7 +3 7

28 +18

29 +19

28 +18

L E A R N A ND C ONNEC T Decimals are another way of writing fractions. We can put a decimal in a place value chart. When a fraction has a denominator of 10, the numerator tells us the number of tenths. Write a 0 before the decimal point. Write the number of tenths after the decimal point.

3 = 10

ones

tenths

0.3 We say three tenths.

Decimal point

AP P LY Write each as a decimal. 1. Five tenths

6 10

9. One tenth

3. Four tenths

6. 10

7. 10

10. Two tenths

11. 10

2. 10

8. Six tenths

12. 10

Decimal - a way to write a number using place value and a decimal point Decimal point - a dot placed between the ones and the tenths places Tenths - the place value position to the right of the decimal point

Level D

| Chapter 13 - 1

Eight tenths

Vocabulary

262

| Lighthouse MATH

Exercise | 13 - 1 Name

Write each as a decimal. 3

1. 10

2. One tenth

5. Six tenths

9. Four tenths

10. 10

3. 10

4. Two tenths

6. 10

7. Nine tenths

8. 10

11. Three tenths

12. Eight tenths

13.

14.

15.

16.

17.

18.

19. Richard got eight out of ten questions correct on his last history quiz. Write his score as a decimal.

Read the problem. Then solve. 20. Kane rode 9 out of the 10 rides at the state fair. Write this amount as a decimal.

CH AL L ENGE Solve. 3

21. Daniel says that 8 is written as the decimal 0.3. Do you agree? Why or why not?

Level D

| Chapter 13 - 1

| Lighthouse MATH

263

13 - 2 | Decimals with Whole Numbers Write each as a decimal. 1.

DAILY REV IE W

Six tenths

6 10

Nine tenths

1 10

Seven tenths

L E A R N A ND C ONNEC T The number of wholes in a mixed number tells us the digits before the decimal. Write the decimal after the ones, then write the number of tenths. When we read the number, the decimal point says "and."

4 = 2 10

ones

tenths

Whole number

Decimal point

2.4 We say two and four tenths.

AP P LY Write a decimal for each number. 1.

264

Level D

| Chapter 13 - 2

| Lighthouse MATH

Exercise | 13 - 2 Name

Write a decimal for each number. 7

1. Six and four tenths

2. Three and seven tenths

3. Eight tenths

5. Eight

6. Four and one tenth

7. Five and 10

9. Four and seven tenths

10. Three and 10

4. 10

8. 10

11. Twelve and 10

12. Two and six tenths

Write each decimal in words.

Four and 16. 3.8

14. 5.9 tenths

and nine tenths 18. 2.7

17. 9.1

Two and

and one tenth

Three and eight 19. 9.2

15. 6.0

20. 1.8

Nine and

13. 4.3

21. 3.5 and eight tenths

Three and

CH AL L ENGE 22. The teacher showed a picture and asked students to write the correct decimal. Kelly’s answer was 1.16 because she said there are 1 and sixteen tenths. Was Kelly correct? Why or why not?

Level D

| Chapter 13 - 2

| Lighthouse MATH

265

13 - 3 | Hundredths Write a decimal. 1. Six tenths DAILY REV IE W

2. One and two tenths

3. Nine tenths

4. One and eight tenths

L E A R N A ND C ONNEC T A fraction with a denominator of 100 can be written as a number with two decimal places. The numerator tells us the number of hundredths. Write the whole number before the decimal point. Write the number of hundredths after the decimal point. If you have 9 or less hundredths you need to put a zero in the tenths place so that the digit ends up in the hundredths place.

3 = 100

33 = 1 100

ones

tenths hundredths

0 ones

tenths hundredths

0.03 We say three hundredths.

1.33 We say one and thirty-three hundredths.

AP P LY Write the decimal for each part. 1.

Vocabulary Hundredths - in place value, the number two to the right of the decimal

266

Level D

| Chapter 13 - 3

| Lighthouse MATH

Exercise | 13 - 3 Name

Write a decimal for each number. 1. 7 100

2. 3 100

3. 100

6. 8 100

10. 5 100

11. 100

5. 10 100 9.

2 100

35 100

7. 100

8. 10 100

12. 7 100

13. Three and twelve hundredths

14. Ten and fourteen hundredths

15. Thirty-five hundredths

16. Ninety-two hundredths

17. Five and two hundredths

18. Two and eighty-nine hundredths

19. Three and fifteen hundredths

20. One hundredth

Write the decimal in words. 22. 2.55

Eight and sixteen

23. 1.06

Two and hundredths 25. 3.04

24. 4.71

One and hundredths

-five

26. 0.81

Three and four

and seventyone hundredths 27. 5.06

28. 0.72

Five and hundredths

21. 8.16

Eighty-one 29. 4.67

hundredths

and hundredths

CH AL L ENGE Write the decimals as fractions. 30. 0.3

31. 0.15

Level D

32. 0.27

33. 0.5

| Chapter 13 - 3

| Lighthouse MATH

34. 0.6

267

13 - 4 | Comparing and Ordering Decimals Write the fractions as decimals. 15 100

DAILY REV IE W

2 100

3 100

6 100

5 100

L E A R N A ND C ONNEC T Which bag weighs more?

Bag A

Bag B

2.21 lbs

2.26 lbs

Line up the decimal points.

First, compare the digits in the highest place value.

If they're the same, move to the right until you find digits that are different and compare them.

2.21 lbs 2.26 lbs

2.21 2.26

2=2

6>1

Bag B weighs more because 2.26 > 2.21.

We can write the weights in order from least to greatest: 2.21 lbs; 2.26 lbs

AP P LY Shade in the models to represent the decimals. Write <, >, or = to compare. 1.

268

0.4

0.04

Level D

0.8

0.6

| Chapter 13 - 4

| Lighthouse MATH

0.3

0.30

Exercise | 13 - 4 Name

Tip!

Write >, <, or = in each circle. 1.

0.74

0.64

Zeros can be added to or dropped from the end of decimals.

0.5

0.39

0.2 = 0.20

1.8

0.43

0.91

0.81

0.34

0.68

6.8

10.5

10.50

0.85

0.58

1.42

1.43

10. 0.04

4.04

11. 0.98

0.89

12. 0.21

0.22

13. 9.7

9.07

14. 3.06

3.60

15. 0.01

0.10

16. 5.6

5.60

1.80

Write the numbers in order from least to greatest.

;

18. 58.4; 54.4; 54.8; 84.5

;

19. 3.33; 3.43; 3.23; 3.13

;

20. 13.15; 15.13; 13.11

21. 37.26; 37.56; 37.36

22. 35.51; 35.15; 35.55

;

23. 10.17; 17.01; 10.71

24. 5.36; 5.16; 5.15

25. 4.07; 4.17; 4.05

;

17. 12.29; 11.26; 12.12

;

CH AL L ENGE 26. David and his friends ran a race. Their times are shown in the chart. Place the runners in order from fastest to slowest.

Level D

David

Eitan

Victor

0.348 minutes

0.342 minutes

0.364 minutes

| Chapter 13 - 4

| Lighthouse MATH

269

13 - 5 | Chapter Review Write as a decimal. 1.

DAILY REV IE W

L E T ' S REV I EW Naming Decimals Fractions and mixed numbers can be written as decimals. The number of wholes comes before the decimal point. The number of tenths or hundredths comes after the decimal.

2 10

0.2

Two tenths

14 100

One and fourteen hundredths

1.14

Comparing Decimals 3.78

Line up the decimal points. Start comparing with the digits in the highest place value. If they are the same, move to the right until the digits are different.

3=3 7>4

3.46 3.78 > 3.46

AP P LY Write each as a decimal. 4

1. 10

2. 10

3. 10

4. Eight tenths

5. Five and three tenths

6. Eight and nine tenths

7. Nine and six tenths

8. Two and seven tenths

270

Level D

| Chapter 13 - 5

| Lighthouse MATH

Exercise | 13 - 5 Name

Write the decimal in words. 1.

4.24 and twentyfour hundredths

6.92 Six and ninety-two

3.05 Three and hundredths

Write the decimal. 4.

7. Nine and sixty-three hundredths

8. Six and eight hundredths

9. Seventy-three hundredths

11. 4100

12. 100

13. 100

10. 8100

Write >, <, or = in each circle. 14. 3.9

3.09

15. 0.7

0.70

16. 0.94

0.49

17. 1.2

0.12

18. 0.6

0.06

19. 2.45

3.54

20. 0.42

0.27

21. 3.29

3.92

Write the numbers in order from least to greatest. 22. 3.62; 3.06; 3.26

23. 12.4; 12.04; 1.24

;

Level D

| Chapter 13 - 5

24. 6.34; 6.04; 6.43; 6.4

;

| Lighthouse MATH

;

271

13 - 6 | Cumulative Review

Solve. 1.

4 × 1

6 + 9

9 − 2

6 + 5

4 × 2

7 + 3

3 × 2

9 × 9

8 + 9

10.

12 − 5

11.

4 − 3

12.

8 + 4

13.

8 + 6

14.

4 + 4

15.

2 × 4

16.

14 − 6

17.

4 + 7

18.

2 + 2

19.

4 × 6

20.

6 × 6

21.

6 × 4

22.

6 × 7

23.

15 − 9

24.

1 × 1

25.

4 + 5

26.

7 − 6

27.

15 − 8

28.

11 − 6

29.

8 × 2

30.

12 − 9

31.

7 + 9

32.

9 × 2

33.

3 − 1

34.

5 × 2

35.

6 + 1

36.

1 × 2

37. 5 5

38. 9 72

39. 8 64

40. 6 36

41. 6 42

42. 1 2

43. 3 27

44. 4 20

45. 6 48

46. 5 15

47. 1 1

48. 4 16

49. 7 35

50. 1 7

51. 4 4

52. 6 18

53. 7 28

54. 3 18

272

Level D

| Chapter 13 - 6

| Lighthouse MATH

Exercise | 13 - 6 Name

Add. 1.

316 + 145

993 + 112

975 + 839

6,887 + 8,790

7,692 + 8,643

314 − 161

963 − 592

8,227 − 7,128

10.

7,699 − 5,588

12.

955 × 7

13.

8,856 × 5

14.

8,855 × 6

15.

97 × 87

Subtract. 6.

544 − 139

Multiply. 11.

448 × 4

Divide. 17. 4 100

18. 2 1,677

19. 5 3,865

16. 7 102

Write the missing numerator. 20.

21.

1 3 = 6

23.

22.

2 5 = 10

24.

1 2 = 4

2 4 = 8

25.

4 6 = 12

Level D

| Chapter 13 - 6

| Lighthouse MATH

1 3 = 9

273

14 C H A P T E R

274

In Chapter 14 we will learn about

Geometry, Measurement, and Data Math can be found in the real world when you build, measure, and use objects of different shapes. It is important to understand the different types of shapes and measurements. • We will learn about lines and angles and how to measure them. • We will learn the different types of triangles and quadrilaterals. • We will learn how to measure perimeter and area of rectangles. • We will understand time of day. • We will understand measures of length. • We will understand measures of volume. • We will understand measures of weight. • We will learn to read dot plots.

275

14 - 1 | Points, Lines, Line Segments, and Rays Compare. DAILY REV IE W

0.37 2.

26 hundredths

0.2

0.20

0.75

1.72

0.9

0.09

L E A R N A ND C ONNEC T Points, lines, line segments, and rays help us draw and describe shapes in geometry. Point

Line

An exact spot

A straight path that goes in both directions

Draw it

Write it

Point W

Write it T

Line Segment

Ray

Part of a line that has two endpoints

Part of a line that has one endpoint and the other side goes on forever in one direction

Draw it

Write it

Draw it

Draw it N

Write it P

AP P LY Use letters and symbols to write the name of each of the following: 1.

276

Level D

| Chapter 14 - 1

| Lighthouse MATH

8. D

Exercise | 14 - 1 Name

Use letters and symbols to write the name of each of the following: 1.

X S

10. UV

11. GH

12. MN

13. KL

14. GH

15. Point E

16. AB

17. Point M

18. RS

19. CD

20. EF

Point R

Draw and label the figures.

CH AL L ENGE Name two line segments on the line below. 21.

Level D

| Chapter 14 - 1

| Lighthouse MATH

277

14 - 2 | Angles Draw and label each of the following: 1.

DAILY REV IE W

Point G

L E A R N A ND C ONNEC T An angle is formed when two lines meet at a shared point. We measure angles in degrees. The ° symbol tells us the angle’s degree measure.

Obtuse angle More than 90°

Right angle Equal to 90°

Acute angle Less than 90°

90 100 110

120

13 0

40 10

170 180 160

150

This angle measures 60º

AP P LY Identify the type of angle and its measurement. 80

90 100 110

120

13 0

90 100 110

10 0

Type of Angle:

Measurement:

Vocabulary Degrees - the unit in which we measure an angle

278

Level D

Protractor - a tool used for measuring angles in degrees

| Chapter 14 - 2

| Lighthouse MATH

13 0

170 180 160

Type of Angle:

120

150

0 14

150

0 14

13 0

170 180 160

120

150

90 100 110

0 14

To measure an angle, use a protractor. One line of the angle is lined up with the bottom of the protractor. To find the measure of the angle, read the number on the protractor that the other line crosses through.

Exercise | 14 - 2 Name

Identify the type of angle and its measurement. 120

13 0

120

Type of Angle:

Measurement:

90 100 110

120

13 0

120

Type of Angle:

Measurement:

90 100 110

120

13 0

90 100 110

120

13 0

120

0 14

150

170 180 160

13 0 150

120

0 14

90 100 110

170 180 160

150

0 14

90 100 110

170 180 160

150

0 14

13 0

120

90 100 110

170 180 160

150

0 14

90 100 110

170 180 160

150

0 14

Type of Angle:

Measurement:

90 100 110

CH AL L ENGE Kayla

Read the problem. Then solve. 10. Ann and Kayla both drew 65° angles. Kayla says that the degree of her angle is larger because her rays are longer. Is she correct?

Level D

| Chapter 14 - 2

| Lighthouse MATH

Ann

279

14 - 3 | Classifying Triangles Name the quadrilateral. 1.

DAILY REV IE W

L E A R N A ND C ONNEC T Triangles come in different shapes. You can tell the type of triangle by its angles and the length of its sides.

Equilateral triangle 3 equal angles 3 equal side lengths

A box shows a right angle.

These marks show sides that are equal.

Isosceles triangle 2 equal angles 2 equal side lengths

Right triangle One angle in the triangle is 90°.

Scalene triangle No equal angles No equal side lengths

AP P LY Circle the right triangles. 1.

10.

Vocabulary Equilateral triangle - a triangle with all three angle measurements and all three side lengths the same Isosceles triangle - a triangle with two angle measurements and two side lengths the same Scalene triangle - a triangle with no angle measurements or side lengths the same Right triangle - a triangle with one right angle

280

Level D

| Chapter 14 - 3

| Lighthouse MATH

Exercise | 14 - 3 Name

Label the triangles as scalene, isosceles, or equilateral based on their sides or angles. 1.

2. 2 yd

2 yd

5 in

3 in

93°

51°

2 in

60°

2 in

5 ft 3 in

60°

36°

3 ft

7 in

2 yd

3 ft

90°

45°

60°

85°

50°

45°

Circle the isosceles triangles. 9.

10.

11.

12.

15.

16.

13.

14.

Circle the scalene triangles.

CH AL L ENGE 17. John says that a right triangle can also be an isosceles triangle. Is he correct or incorrect? Explain why.

Level D

| Chapter 14 - 3

| Lighthouse MATH

281

14 - 4 | Classifying Quadrilaterals Identify the type of angle and its measurement. 90 100 110

120

3. 13 0

90 100 110

120

13 0

0 14

150

170 180 160

150

170 180 160

0 14

150

50 0 14

DAILY REV IE W

2. 13 0

120

90 100 110

Type of Angle:

Measurement:

L E A R N A ND C ONNEC T These lines are parallel. They will never meet.

Quadrilaterals have four sides.

Parallelogram

Has two sets of parallel sides

Trapezoid Has one set of parallel sides

Rectangle

Rhombus

A parallelogram with four right angles

A parallelogram with all sides equal

Square

Is a rhombus and a rectangle

These lines are not parallel. They will meet.

Kite

Has no parallel sides

AP P LY Write the names of the shapes. 1. Which shapes have two sets of parallel sides? 2. Which shapes have four sides that are the same length? 3. Which shapes have four right angles? 4. Which shapes have one set of parallel sides? Vocabulary Trapezoid - a quadrilateral with one set of parallel sides Rhombus - a quadrilateral with four equal sides and opposite sides that are parallel

282

Level D

Rectangle - a quadrilateral with four right angles and opposite sides that are equal and parallel Square - a rectangle with all equal sides Parallelogram - a quadrilateral with opposite sides equal and parallel and opposite angles equal

| Chapter 14 - 4

| Lighthouse MATH

Exercise | 14 - 4 Name

Circle all the words that describe the shape. 2.

parallelogram

rectangle

square

rhombus

trapezoid

parallelogram

rectangle

square

rhombus

trapezoid

kite

trapezoid

CH AL L ENGE 7. Tell one way a parallelogram and a trapezoid are different.

Level D

| Chapter 14 - 4

| Lighthouse MATH

283

14 - 5 | Perimeter and Area Write the type of triangle shown. 1.

DAILY REV IE W

L E A R N A ND C ONNEC T Perimeter is the distance around a shape.

12 ft 8 ft

Area is the amount of space a shape takes up. Add up all the sides to find the perimeter.

Multiply the length by the width to find the area.

8 ft 12 ft

12 ft

8 ft

1 square foot:

8 ft

P = 12 + 12 + 8 + 8 P = 40 ft

We measure area in square units.

1 ft

A = 12 × 8 A = 96 square feet

1 ft

AP P LY Find the area and perimeter of each shape. 6 cm

9 in

2 cm

3 in

Perimeter =

Area =

Vocabulary Area - the measure inside a flat shape (length × width) Perimeter - the measure around an object (length + width + length + width)

284

Level D

| Chapter 14 - 5

| Lighthouse MATH

Exercise | 14 - 5 Name

Find the area and perimeter of each figure. 16 ft

2. 6 ft

25 ft

44 yd

9 ft

21 yd

Perimeter =

Area =

6. 7 ft

4 cm

14 ft

8 cm

14 ft

3 ft

Perimeter =

Area =

8. 10 m

9. 6 ft

8 ft 20 m

5 ft

15 ft

Perimeter =

Area =

CH AL L ENGE 6m

Find the area and perimeter of this figure. 10. Area =

20 m 10 m

Perimeter =

24 m

Level D

| Chapter 14 - 5 | Lighthouse MATH

285

14 - 6 | Understanding Time of Day Find the area and perimeter of the rectangles. 1.

1 ft

DAILY REV IE W

2m 4m

2 ft

4 ft

6 ft

Area =

Perimeter =

L E A R N A ND C ONNEC T 11 p.m.

There are 24 hours in a day. The first 12 hours are called a.m. The next 12 hours are called p.m. Midnight is 12:00 a.m. It starts the a.m. hours. Noon is 12:00 p.m. It starts the p.m. hours.

10 p.m. midnight ep asle

9 p.m. 8 p.m.

de sleeep p

p.m. hours

r dinne e comm 5 p.m. fsrochool

3 a.m.

6 a.m.

sc ho ol

2 p.m.

5 a.m.

waking up bre akfa st

3 p.m.

It makes sense to be sleeping at 2:00 a.m.

n early daw

a.m. hours

4 p.m.

3 hours after 11:00 p.m. is 2:00 a.m.

2 a.m.

4 a.m.

7 p.m.

1 a.m.

ge reat for bdy ed

6 p.m. 11

12:00 a.m. Midnight

7 a.m. 8 a.m.

9 a.m.

10 a.m. 1 p.m.

lunch

11 a.m.

Noon 12:00 p.m.

AP P LY Circle the time that makes the most sense. 1.

5 a.m.

286

5 p.m.

12 a.m.

Level D

| Chapter 14 - 6

12 p.m.

| Lighthouse MATH

1 a.m.

1 p.m.

Exercise | 14 - 6 Name

Circle the time that makes the most sense. 1.

8 a.m.

8 p.m.

10 a.m.

10 p.m.

5 a.m.

1 a.m.

1 p.m.

2 a.m.

2 p.m.

5 p.m.

8 a.m.

8 p.m.

Write the time. Write a.m. or p.m.

p. m .

2 hours after 8:00 p.m.

1 hour after 12:00 a.m.

4 hours after 11 p.m.

10. 6 hours after 6:00 a.m.

11. 1 hour before 5:00 a.m.

12. 2 hours before 11:00 p.m.

13. 3 hours before 2:00 a.m.

14. 2 hours before 12:00 p.m.

a. m .

CH AL L ENGE 15. Donald started reading at half past eleven at night. He read for ninety-five minutes. What time did Donald finish reading? Donald finished reading at

Level D

| Chapter 14 - 6

| Lighthouse MATH

287

14 - 7 | Inches, Feet, Yards, Miles Solve. 1.

DAILY REV IE W

687 ÷ 9

12 × 9

31 × 6

87 ÷ 6

52 × 7

L E A R N A ND C ONNEC T Length tells us how long an object is. We use tools like rulers, yardsticks, and tape measures to measure inches, feet, and yards. We use miles to measure long distances, like the distance between towns, cities, or places.

Units of Length 1 inch 1 foot = 12 inches

1 yard = 3 feet 1 yard = 36 inches

The wood stick is 4 feet long. Each foot is 12 inches. 4 × 12 = 48 The stick is 48 inches.

1 mile = 5,280 feet

AP P LY Circle the best estimate. 1. Height of a tree

30 feet

2. Length of a field

30 miles

4. Length of a car

10 inches

120 yards

3. Height of a door

120 inches

5. Length of a pencil

10 feet

6 inches

7 feet

7 inches

6. Width of a window

6 yards

36 yards

36 inches

Vocabulary 1

Inch - a unit of measurement equal to 12 of a foot or 36 of a yard Mile - a unit of measurement equal to 5,280 feet

288

Level D

Foot - a unit of measurement equal to 12 inches or 3 of a yard Yard - a unit of measurement equal to 36 inches or 3 feet

| Chapter 14 - 7

| Lighthouse MATH

Exercise | 14 - 7 Name

Convert the measurements. 1.

3 yards =

inches

3 yards =

feet

9 feet =

inches

1 mile =

feet

9 yards =

feet

2 yards =

feet

4 yards =

feet

3 feet =

inches

2 miles =

feet

10. 7 feet =

inches

11. 12 feet =

inches

12. 5 yards =

feet

13. 3 miles =

feet

14. 6 feet =

inches

15. 2 feet =

inches

16. 10 feet =

inches

17. 11 feet =

inches

18. 8 yards =

feet

19. 4 feet =

inches

20. 10 yards =

feet

21. 8 feet =

inches

22. 5 feet =

inches

23. 1 foot =

inches

24. 6 yards =

feet

25. 30 yards

90 feet

26. 24 inches

2 feet

27. 9 yards

28. 1 mile

5,000 feet

29. 25 feet

10 yards

30. 25 inches

2 feet

31. 2 yards

20 feet

32. 4 yards

15 feet

33. 75 inches

5 feet

Write <, >, or = to compare the measurements. 18 feet

CH AL L ENGE Convert the measurements. 34. 3 yards =

35. 2 miles =

inches

Level D

| Chapter 14 - 7

| Lighthouse MATH

inches

289

14 - 8 | Cups, Pints, Quarts, Gallons Write the equivalent units. DAILY REV IE W

5 feet =

inches

1 yard =

inches

5,280 feet =

mile

L E A R N A ND C ONNEC T Liquid capacity tells us how much space a liquid takes up. We use tools like spoons, cups, bottles, and buckets to measure cups, pints, quarts, and gallons.

Units of Capacity 1 fl ounce 1 cup = 8 fl ounces

6 gallon 5 gallon 4 gallon 3 gallon 2 gallon 1 gallon

There are 4 gallons of floor cleaner. Each gallon is 4 quarts.

1 pint = 2 cups 1 quart = 2 pints

4 × 4 = 16 There are 16 quarts of floor cleaner.

1 gallon = 4 quarts

AP P LY

Circle the best estimate. 1.

1 ounce

1 quart

16 ounces

16 cups

1 pint

1 gallon

1 pint

1 gallon

4 pints

4 gallons

8 ounces

80 ounces

Vocabulary Gallon - a unit of measurement for liquids; equal to 4 quarts or 8 pints 1 Fluid ounce - a unit of measurement for liquids; equal to 8 of a cup 1 Quart - a unit of measurement for liquids; equal to 2 pints or 4 of a gallon

290

Level D

| Chapter 14 - 8

Pint - a unit of measurement for liquids; equal to 16 ounces or 2 of a quart Cup - a unit of measurement for liquids; equal to 8 fluid ounces

| Lighthouse MATH

Exercise | 14 - 8 Name

Convert the measurements. 2.

3 pints =

cups

9 cups =

fl ounces

quarts

4 cups =

fl ounces

7 gallons =

quarts

pints

4 pints =

cups

4 gallons =

quarts

10. 6 gallons =

quarts

11. 5 pints =

cups

12. 5 cups =

13. 7 quarts =

pints

14. 10 cups =

fl ounces

15. 10 gallons =

16. 10 quarts =

pints

17. 6 quarts =

pints

18. 12 pints =

cups

19. 3 quarts =

pints

20. 4 quarts =

pints

21. 8 pints =

cups

22. 2 gallons =

quarts

23. 9 gallons =

quarts

24. 12 quarts =

pints

4 cups

27. 24 fl ounces

3 cups

2 pints =

3 gallons =

2 quarts =

cups

fl ounces

quarts

25. 10 quarts

30 pints

26. 32 fl ounces

28. 11 gallons

36 quarts

29. 25 cups

10 pints

30. 25 fl ounces

2 cups

31. 3 quarts

10 pints

32. 2 pints

9 cups

33. 75 fl ounces

20 cups

36. 5 quarts =

cups

CH AL L ENGE Convert the measurements. 34. 2 gallons =

cups

35. 5 pints =

Level D

| Chapter 14 - 8

fl ounces

| Lighthouse MATH

291

Write <, >, or = to compare the measurements.

14 - 9 | Ounces, Pounds, Tons Compare the measurements using <, >, or =. DAILY REV IE W

10 cups

2 quarts

32 fl ounces

3 pints

5 cups

3 quarts

L E A R N A ND C ONNEC T Weight tells us how heavy something is. We use a scale to measure ounces, pounds, and tons.

Units of Weight

1 ounce

The elephant weighs 3 tons. Each ton is 2,000 pounds.

1 pound = 16 ounces

3 × 2,000 = 6,000 The elephant weighs 6,000 pounds.

1 ton = 2,000 pounds

AP P LY Circle the best estimate. 1.

2 ounces

2 tons

6 pounds

6 ounces

1 ton

1 pound

200 tons 6.

10 pounds

10 ounces

8 tons

Vocabulary 1

Ounce (oz) - a unit of weight that equals 16 of a pound Pound (lb) - a unit of weight that equals 16 ounces

292

Level D

200 ounces

Ton (t) - a unit of weight that equals 2,000 pounds

| Chapter 14 - 9

| Lighthouse MATH

8 pounds

Exercise | 14 - 9 Name

Convert the measurements. 1.

6 pounds =

ounces

4 tons =

pounds

11 pounds =

ounces

15 tons =

pounds

3 pounds =

ounces

9 tons =

pounds

8 pounds =

ounces

2 tons =

pounds

14 pounds =

ounces

pounds

11. 5 pounds =

ounces

12. 18 tons =

pounds

ounces

10. 7 tons = 13. 10 pounds =

ounces

14. 3 tons =

pounds

15. 20 pounds =

16. 12 tons =

pounds

17. 4 pounds =

ounces

18. 8 tons =

pounds

19. 2 pounds =

ounces

20. 10 tons =

pounds

21. 9 pounds =

ounces

2 tons

24. 3 pounds

30 ounces

4 pounds

22. 10 ounces 25. 6,000 pounds 28. 4 pounds

30 pounds

23. 4,000 pounds

3 tons

26. 34 ounces

2 pounds

27. 64 ounces

16 ounces

29. 18 ounces

2 pounds

30. 5,000 pounds

3 tons

CH AL L ENGE Solve. 31. Jake’s truck weighs 5,000 pounds when it is empty. How many tons is that?

Level D

| Chapter 14 - 9

| Lighthouse MATH

293

Write <, >, or = to compare the measurements.

14 - 10 | Dot Plots Compare using <, >, or =. DAILY REV IE W

1. 64 ounces

5 pounds

2. 10,000 pounds

3 tons

3. 10 ounces

L E A R N A ND C ONNEC T A dot plot is a graph that shows dots above a number line.

Sara measured the flowers in her garden. Heights of flowers in inches: 13, 13, 12, 12, 12, 12, 13, 11, 14, 12, 11, 14, 12, 13, 10, 12, 15, 11, 13, 14, 13, 13, 12, 11, 15, 12, 13, 15, 14, 10

She makes one dot for each flower. She places it over the number that shows its height.

Title

Height of Flowers in Sara's Garden

Number line

Height of Flowers in Inches

AP P LY Use the dot plot above to answer the following questions. 1. How many flowers measured 10 inches?

2. How tall is the tallest flower?

3. How many flowers measured 12 inches?

4. What is the most common height of the flowers?

5. How many flowers measured 15 inches?

6. What is the least common height of the flowers?

Vocabulary Dot plot - a graph that shows data as marks above a number line, showing each value’s frequency

294

Level D

| Chapter 14 - 10

| Lighthouse MATH

Number line label

2 pounds

Exercise | 14 - 10 Name

Use the dot plots to answer the questions. Students in an After-School Program

1. The dot plot shows the ages of students in an after-school program. A. How many students are 9 years old? B. How many students are there in all?

C. What is the least common age?

Ages of Students

2. A company asked its workers how long it takes them to get to work each day. The results are shown on the dot plot below. Worker Travel Times

A. How many workers did the company ask? B. What is the difference between the longest and shortest travel times? C. How many people said it takes 3 them 4 hour or more to travel to work?

1 4

2 4

3 4

11 4

12 4

Time Traveling (hours)

3. Mr. Smith’s class recorded how much time they spent reading each week on the dot plot below. A. How many students are in Mr. Smith’s class?

Class Reading Times

B. What is the difference between the most reading time and the least reading time? 1 2

C. How many students read for at least an hour?

11 2

21 2

Hours Spent Reading

CH AL L ENGE Use Mr. Smith’s dot plot to answer the following question. 1

4. Two new students joined the class. One said he read for 4 2 hours a week, 1 and the other said he read for 3 2 hours per week. How many hours did the class read in total with the addition of the two new students?

Level D

| Chapter 14 - 10

| Lighthouse MATH

295

14 - 11 | Chapter Review Write the name of the figure. 1.

DAILY REV IE W

L E T ' S REV I EW Angles X

Find Area and Perimeter of a Rectangle

Right 90°

Perimeter: Add the lengths of the sides. Area: Multiply the length by the width. l

Acute Less than 90°

Obtuse Greater than 90°

Perimeter = l + l + w + w Area = l × w

w l

Converting Between Units of Measurements Volume 1 gallon = 4 quarts 1 quart = 2 pints 1 pint = 2 cups 1 cup = 8 fl ounces

Weight 1 ton = 2,000 pounds 1 pound = 16 ounces

AP P LY Identify the type of angle and its measurement. Type of Angle:

13 0

2. 50

90 100 110

Write the type of triangle. 3.

296

Level D

| Chapter 14 - 11

120

Type of Angle:

13 0

170 180 160

Measurement:

120

90 100 110

150

170 180 160

150

0 14

Length 1 foot = 12 inches 1 yard = 3 feet 1 yard = 36 inches 1 mile = 5,280 feet 1 mile = 1,760 yards

| Lighthouse MATH

Measurement:

Exercise | 14 - 11 Name

Circle all the words that describe the shape. 1.

Parallelogram

Square

Trapezoid

Rectangle

Kite

Square

Rhombus

Find the area and perimeter of each shape. 4.

14 ft

11 ft

8 ft

30 ft

24 yd

18 yd

Area =

Perimeter =

3 yards =

inches

2 yards =

feet

7 feet =

Convert the measurements. inches

Use the dot plot to answer the questions. 10. How many students read for 45 minutes?

Class Reading Times

11. What is the difference between the longest time spent reading and the shortest time?

Hours Spent Reading

Level D

| Chapter 14 - 11

| Lighthouse MATH

297

14 - 12 | Cumulative Review

Solve. 1.

2 + 2

1 + 2

3 + 1

8 + 6

3 × 2

6 × 6

7 + 9

8 + 1

12 − 9

10.

4 + 9

11.

2 × 2

12.

15 − 6

13.

6 × 1

14.

4 × 9

15.

9 + 2

16.

6 + 3

17.

6 × 4

18.

4 + 8

19.

6 × 7

20.

9 − 2

21.

6 × 2

22.

1 + 3

23.

2 + 9

24.

1 × 2

25.

3 − 1

26.

3 × 9

27.

2 × 9

28.

15 − 7

29.

4 + 2

30.

2 + 6

31.

13 − 9

32.

5 × 7

33.

15 − 9

34.

7 × 7

35.

4 − 3

36.

6 + 7

37. 6 12

38. 4 48

39. 7 14

40. 8 16

41. 2 6

42. 4 4

43. 2 12

44. 5 15

45. 6 42

46. 3 24

47. 9 9

48. 9 45

49. 7 7

50. 8 40

51. 5 25

52. 6 24

53. 8 24

54. 9 81

298

Level D

| Chapter 14 - 12

| Lighthouse MATH

Exercise | 14 - 12 Name

Add. 1.

509 + 697

487 + 729

420 + 295

5,247 + 7,941

9,372 + 4,699

982 − 166

575 − 441

9,716 − 7,770

10.

9,696 − 8,203

12.

657 × 3

13.

1,338 × 5

14.

4,123 × 9

15.

36 × 12

Subtract. 6.

734 − 146

Multiply. 11.

610 × 8

Divide. 16. 8 577

17. 5 210

18. 8 2,283

19. 6 4,044

20.

21. 1

22. 2

Shade 5 . 2 Shade another 5 .

Shade 6 . 1 Shade another 6 .

Shade 10 . 3 Shade another 10 .

1 2 5 + 5 =

2 1 6 + 6 =

4 3 10 + 10 =

23.

24.

25.

Shade 9 . 3 Shade another 9 .

Shade 4 . 2 Shade another 4 .

Shade 7 . 3 Shade another 7 .

2 3 9 + 9 =

1 2 4 + 4 =

3 3 7 + 7 =

Level D

Shade. Then add to find the total.

| Chapter 14 - 12

| Lighthouse MATH

299

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